{"id":7,"date":"2023-09-17T11:16:54","date_gmt":"2023-09-17T11:16:54","guid":{"rendered":"https:\/\/mathority.org\/id\/fungsi-parabola-kuadrat\/"},"modified":"2023-09-17T11:16:54","modified_gmt":"2023-09-17T11:16:54","slug":"fungsi-parabola-kuadrat","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/fungsi-parabola-kuadrat\/","title":{"rendered":"Fungsi kuadrat atau parabola"},"content":{"rendered":"<p>Halaman ini menjelaskan apa itu fungsi kuadrat beserta seluruh ciri-cirinya: kelengkungan, titik sudut, titik potong dengan sumbu, dll. Anda juga akan mempelajari cara merepresentasikan fungsi kuadrat pada grafik. Dan terakhir, Anda dapat berlatih dengan contoh, latihan langkah demi langkah, dan soal fungsi kuadrat. <\/p>\n<p><strong><\/strong><\/p>\n<p><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-104\"><strong> <\/strong><\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-una-funcion-cuadratica\"><\/span> Apa itu fungsi kuadrat? <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-105\"><strong> <\/strong><\/div>\n<\/div>\n<p>Pengertian fungsi kuadrat adalah sebagai berikut: <\/p>\n<div style=\"padding-top: 23px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 30px; border: 2px dashed #FF9B28; border-radius:20px;\">\n<p style=\"text-align:left\"> Dalam matematika, <strong>fungsi kuadrat (atau parabola)<\/strong> adalah fungsi polinomial berderajat 2, yaitu fungsi yang suku derajat tertingginya berpangkat kedua. Oleh karena itu, rumus fungsi kuadrat adalah:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-576d742ea12f780a76fa5809f5112086_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=ax^2+bx+c\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"154\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\"> Emas:<\/p>\n<ul>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0dfe37f98696a04358a5783f12ff4d6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"ax^2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"26\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah suku kuadrat.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e925448cc849aa310b3d4a7b77594e4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"bx\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah istilah linier.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah istilah independen.<\/li>\n<\/ul>\n<\/div>\n<p> Domain suatu fungsi kuadrat selalu terdiri dari bilangan real. <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-91d461485d0f02bb14db6855a3774878_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f=\\mathbff{R}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"concavidad-y-convexidad-de-una-funcion-cuadratica\"><\/span> Kecekungan dan konveksitas suatu fungsi kuadrat<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Menganalisis kelengkungan fungsi kuadrat atau parabola sangatlah sederhana, karena hanya bergantung pada koefisien kuadrat.<\/p>\n<ul>\n<li> Jika koefisien\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> positif, fungsi kuadratnya <strong>cembung<\/strong> (dalam bentuk<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f5ebc563dbe58138d1de6b7fe99e8d31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{\\cup}\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> ). Oleh karena itu, KTT ini bersifat minimum.<\/li>\n<li> Jika koefisien\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> negatif, fungsi kuadratnya <strong>cekung<\/strong> (berbentuk seperti<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dccbfcebef91876585ebd365457c3d24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{\\cap}\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> ). Oleh karena itu, puncaknya adalah maksimum. <\/li>\n<\/ul>\n<div class=\"wp-block-columns is-layout-flex wp-container-349\">\n<div class=\"wp-block-column is-layout-flow\">\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/fonction-quadratique-ou-parabole-convexe.webp\" alt=\"fungsi kuadrat atau parabola cembung\" class=\"wp-image-132\" width=\"254\" height=\"259\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/fonction-quadratique-ou-parabole-concave.webp\" alt=\"fungsi kuadrat atau parabola cekung\" class=\"wp-image-133\" width=\"255\" height=\"260\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<\/div>\n<\/div>\n<p> <strong>Catatan:<\/strong> Komunitas matematika masih belum sepenuhnya setuju dan, oleh karena itu, beberapa profesor mengatakan sebaliknya: mereka menyebut suatu fungsi cekung yang berbentuk a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f5ebc563dbe58138d1de6b7fe99e8d31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{\\cup}\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> , dan fungsi cembung yang berbentuk<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dccbfcebef91876585ebd365457c3d24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{\\cap}\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> . Pokoknya yang penting bentuknya apa fungsinya, apapun namanya. <\/p>\n<p><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-106\"><strong> <\/strong><\/div>\n<p><strong><br \/><\/strong><\/p>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"vertice-de-una-funcion-cuadratica\"><\/span> Titik puncak fungsi kuadrat<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Untuk membuat grafik fungsi kuadrat, perlu diketahui koordinat titik puncak parabola. <\/p>\n<div style=\"padding-top: 23px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 30px; border: 2px dashed #FF9B28; border-radius:20px;\">\n<p style=\"text-align:left\"> Untuk mencari titik puncak suatu fungsi kuadrat, kita perlu menghitung koordinat X suatu titik dengan menggunakan rumus berikut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-93ad079a75f2c2a452e1aaf0654aaaf1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle x=\\frac{-b}{2a}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"58\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<p> Kemudian kita dapat mencari koordinat titik lainnya dengan menghitung bayangan fungsi pada titik tersebut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8ad3822f13f081a20e55c52589118288_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f\\left(\\frac{-b}{2a}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"62\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Jadi koordinat titik puncak suatu fungsi kuadrat (atau parabola) adalah: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-37777c8a435f1df10f87842c8bd463d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(\\frac{-b}{2a} \\ , \\ f\\left(\\frac{-b}{2a}\\right)\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"130\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"puntos-de-corte-con-los-ejes-de-una-funcion-cuadratica\"><\/span> Titik potong dengan sumbu fungsi kuadrat <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-107\"><strong> <\/strong><\/div>\n<\/div>\n<div style=\"padding-top: 23px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 30px; border: 2px dashed #FF9B28; border-radius:20px;\">\n<p style=\"text-align:left\"> Parabola selalu memotong sumbu y (sumbu Y), dan hal ini terjadi ketika<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d6889ee3f02f0af137641306363d2da7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=0.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\"><\/p>\n<p> Oleh karena itu, untuk menghitung titik potong suatu fungsi kuadrat dengan sumbu Y harus diselesaikan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d449eebd1f011aebdf90931f3a66a3b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(0).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"38\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<\/div>\n<p> Misalnya titik potong fungsi kuadrat berikut dengan sumbu OY adalah: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7a32a12ecec8c6b0617daf9e84bd4d07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^2-2x+1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"146\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9d17bae0af24be9eaa8833d402a1709c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(0)=0^2-2\\cdot 0+1 = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"188\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-308d0aeca611c20e62ee56db1ced4618_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(0,1)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"38\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div style=\"padding-top: 23px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 30px; border: 2px dashed #FF9B28; border-radius:20px;\">\n<p style=\"text-align:left\"> Sebaliknya, titik potong suatu fungsi kuadrat dengan sumbu x (sumbu X) terjadi ketika<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ae937c042e388c1f5126fceae07be7ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=0.\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"71\" style=\"vertical-align: -5px;\"><\/p>\n<p> Jadi untuk menghitung titik potong dengan sumbu X Anda harus menyelesaikan persamaannya<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ae937c042e388c1f5126fceae07be7ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=0.\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"71\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<\/div>\n<p> Sebagai contoh, di bawah ini adalah perhitungan titik potong dengan sumbu OX fungsi kuadrat yang sama:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7a32a12ecec8c6b0617daf9e84bd4d07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^2-2x+1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"146\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-62b9becef089451225ec98e56e46fb45_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"0=x^2-2x+1\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"121\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p> Kami menyelesaikan persamaan kuadrat dengan rumus umum:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bd0f7a0d21b888b4e5016eb027b534a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\cfrac{-b\\pm \\sqrt{b^2-4ac}}{2a}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"165\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c8fa2c0e690ee979b162d63c9ee18904_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\cfrac{-(-2)\\pm \\sqrt{(-2)^2-4\\cdot 1\\cdot1}}{2\\cdot 1} =\\cfrac{2\\pm 0}{2} = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"348\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Maka titik potong fungsi kuadrat dengan sumbu X adalah:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-84f3677bb18b0fdcb23f9f99693d049e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(1,0)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"38\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Dalam kasus ini, kita hanya mendapatkan satu solusi persamaan kuadrat, namun kita bisa mendapatkan dua solusi. Dalam hal ini berarti fungsi kuadrat memotong sumbu X di dua titik berbeda. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-representar-una-funcion-cuadratica-o-parabola\"><\/span> Contoh representasi fungsi kuadrat atau parabola <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-108\"><strong> <\/strong><\/div>\n<p><strong><br \/><\/strong><\/p>\n<\/div>\n<p>Mari kita lihat <strong>cara merepresentasikan fungsi kuadrat<\/strong> pada grafik menggunakan sebuah contoh.<\/p>\n<ul>\n<li> Grafik fungsi berikut:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-daee208a4b18c835d0b39c0a1bbc1ba2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^2-4x+5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"146\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Hal pertama yang harus dilakukan adalah <strong>menghitung titik puncak parabola.<\/strong> Untuk melakukan ini, kami menggunakan rumus yang kami lihat di atas:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c7b3ed3c7bf6661b563290769c1b3f75_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x = \\cfrac{-b}{2a} = \\cfrac{-(-4)}{2\\cdot 1}= \\cfrac{4}{2}= 2\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"215\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Setelah kita mengetahui di mana titik puncaknya, kita perlu membuat tabel nilai: <strong>&nbsp;<\/strong> Kita menghitung nilai fungsi pada titik puncak dan titik-titik di sekitarnya:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-daee208a4b18c835d0b39c0a1bbc1ba2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^2-4x+5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"146\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-352\">\n<div class=\"wp-block-column is-layout-flow\">\n<ul>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-20fbda178bf7ed0b06d87f8b9558352b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 2 \\ \\longrightarrow \\ f(2) = 2^2-4\\cdot2+5=1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"281\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<\/ul>\n<ul>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2561b16ae2d9dc6ea4f9734bedbcdf81_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 1 \\ \\longrightarrow \\ f(1)=1^2-4\\cdot1+5=2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"281\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<\/ul>\n<ul>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-790d7ae514d18f03db8e9c373adbf050_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 3 \\ \\longrightarrow \\ f(3) = 3^2-4\\cdot3+5=2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"281\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<\/ul>\n<ul>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6820340ec293e65b9be9ed3e85ce8308_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 0 \\ \\longrightarrow \\ f(0) = 0^2-4\\cdot0+5=5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"281\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<\/ul>\n<ul>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2b61ea6ec8c7982dc52816f3e27e1637_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 4 \\ \\longrightarrow \\ f(4) = 4^2-4\\cdot4+5=5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"281\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<\/ul>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-361c835cbcad63310e504c58d5d603c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c|c} x &amp; f(x) \\\\ \\hline 2 &amp; 1 \\\\ 1 &amp; 2 \\\\ 3 &amp; 2 \\\\ 0 &amp; 5 \\\\ 4 &amp; 5 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"134\" width=\"78\" style=\"vertical-align: -62px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p> Anda juga dapat menghitung titik potong fungsi kuadrat dengan sumbu Cartesian untuk menggambar parabola dengan lebih baik, namun hal ini tidak sepenuhnya diperlukan.<\/p>\n<p> Kami sekarang mewakili titik-titik yang diperoleh pada grafik <strong>:<\/strong> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-comment-representer-une-fonction-quadratique-ou-parabole.webp\" alt=\"contoh cara merepresentasikan fungsi kuadrat atau parabola\" class=\"wp-image-136\" width=\"260\" height=\"300\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Dan terakhir, kita gabungkan titik-titik tersebut membentuk parabola. Kemudian kita memanjangkan cabang-cabang parabola untuk menunjukkan bahwa ia berlanjut ke atas: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/representation-d-une-fonction-quadratique-ou-parabole.webp\" alt=\"representasi fungsi kuadrat atau parabola\" class=\"wp-image-137\" width=\"260\" height=\"293\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-funciones-cuadraticas\"><\/span> Latihan soal fungsi kuadrat<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> Latihan 1<\/h3>\n<p> Tentukan titik puncak fungsi kuadrat berikut: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d138d20f23c7aa6367c85907671a073b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=2x^2+8x+4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"156\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Lihat solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Kita hitung terlebih dahulu koordinat X titik tersebut dengan menggunakan rumus:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f393ada7f0e57fd87a582657183d4f2b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x = \\cfrac{-b}{2a} = \\cfrac{-8}{2\\cdot 2} = \\cfrac{-8}{4} = -2\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"223\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan sekarang kita menghitung koordinat lainnya dengan mengevaluasi fungsi di titik tersebut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d6067325564a5af06f7384d76157f3aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} f(-2) &amp; =2(-2)^2+8(-2)+4 \\\\[1.7ex] &amp; = 2 \\cdot 4 - 16 +4 \\\\[1.7ex] &amp; = 8-16+4 \\\\[1.7ex] &amp; = -4 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"136\" width=\"221\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, titik puncak fungsi kuadrat adalah: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-331c4c81f99a9749f15d457746a5f745_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-2,-4)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Latihan 2 <\/h3>\n<p><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-110\"><strong> <\/strong><\/div>\n<p><strong><br \/><\/strong><\/p>\n<\/div>\n<p>Temukan titik potong fungsi berikut dengan sumbu: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9c09640c22a09e153b538a5aff018e02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^2-4x+3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"147\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Lihat solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Untuk menghitung titik potong dengan sumbu Y, kita perlu melakukan perhitungan <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8f92d7beea0ed3a053927c2d429d3450_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(0):\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"42\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2b60958618b8dddf8706873a570491dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(0)=0^2-4\\cdot 0+3 = 3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"189\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, fungsi tersebut melalui sumbu Y di titik:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fce94a71978b3cf055b18dce85b4746f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(0,3)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"38\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan untuk mencari titik potong dengan sumbu X kita perlu menyelesaikannya <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-05bb421b504b7ae4aa483574cd6f28d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=0:\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"76\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9c09640c22a09e153b538a5aff018e02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^2-4x+3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"147\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6d78e40252b245c2ea862b8de892b646_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"0=x^2-4x+3\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"122\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Kita menghitung akar-akar persamaan kuadrat dengan rumus: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bd0f7a0d21b888b4e5016eb027b534a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\cfrac{-b\\pm \\sqrt{b^2-4ac}}{2a}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"165\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0d909ba6581faf5916f0b1c0df7e471f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle x=\\cfrac{-(-4)\\pm \\sqrt{(-4)^2-4\\cdot 1\\cdot 3}}{2\\cdot 1} =\\cfrac{4\\pm 2}{2} = \\begin{cases} 3 \\\\[2ex] 1 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"365\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, fungsinya memotong sumbu X di dua titik: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-30411245eaebedd735c4c804372a58e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(1,0) \\qquad (3,0)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"112\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Latihan 3<\/h3>\n<p> Gambarkan fungsi kuadrat berikut: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2dea5d0b581ec4e3a7e39ff51b8a25b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=-x^2+4x+1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"160\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Lihat solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Ini adalah fungsi kuadrat. Oleh karena itu, untuk menyatakannya harus terlebih dahulu menghitung absis titik sudut parabola dengan rumus:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e0d4a78b32998cdd3b2bdff7d143e870_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x = \\cfrac{-b}{2a} = \\cfrac{-4}{2\\cdot (-1)} = \\cfrac{-4}{-2} = 2\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"236\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang kita membuat tabel nilai. Untuk melakukan ini, kami menghitung nilai<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a7ee323bc5a3f73ad5e066b13bed5504_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"34\" style=\"vertical-align: -5px;\"><\/p>\n<p> di atas dan di sekitar atas: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-355\">\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-44c68320944b905e1f9bdc40e71de785_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 2 \\ \\longrightarrow \\ f(2)=-2^2+4\\cdot2+1 = 5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"294\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b8a73224d11487e6153b9fce73715cbb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 1 \\ \\longrightarrow \\ f(1)=-1^2+4\\cdot1+1 = 4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"295\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1db5d9c522aa5f555daed75308f9f5d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 3 \\ \\longrightarrow \\ f(3)=-3^2+4\\cdot3+1 =4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"295\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8011dabdadc4055e9bb1d225a5ce0630_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 0 \\ \\longrightarrow \\ f(0)=-0^2+4\\cdot0+1 = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"294\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ce78a26ab2e830c17be7b66a4d1092a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 4 \\ \\longrightarrow \\ f(4)=-4^2+4\\cdot4+1 = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"294\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-32fd0aec4a82615193ca7a894555a8fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c|c} x &amp; f(x) \\\\ \\hline 2 &amp; 5 \\\\ 1 &amp; 4 \\\\ 3 &amp; 4 \\\\ 0 &amp; 1 \\\\ 4 &amp; 1 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"134\" width=\"78\" style=\"vertical-align: -62px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Dan terakhir, kita plot titik-titik pada grafik dan menggambar parabola: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-fonction-quadratique.webp\" alt=\"contoh fungsi kuadrat\" class=\"wp-image-138\" width=\"267\" height=\"273\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> Latihan 4<\/h3>\n<p> Gambarkan fungsi kuadrat berikut: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-743023f52acec123a62e655d6e2d954d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=-2x^2-8x-1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"169\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Lihat solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Ini adalah fungsi urutan kedua. Oleh karena itu, untuk menyatakannya harus dicari terlebih dahulu absis titik puncak parabola dengan rumus:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7b29662b7e8b1efcbc7ccdccbb082a2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x = \\cfrac{-b}{2a} = \\cfrac{-(-8)}{2\\cdot (-2)} = \\cfrac{+8}{-4} = -2\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"250\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang kita membuat tabel nilai. Untuk melakukan ini, kami menghitung nilai<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a7ee323bc5a3f73ad5e066b13bed5504_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"34\" style=\"vertical-align: -5px;\"><\/p>\n<p> di atas dan di sekitar atas: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-358\">\n<div class=\"wp-block-column is-layout-flow\" style=\"flex-basis:66.66%\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e77f3b13fa69e6004d7032fec18a3904_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= -2 \\ \\longrightarrow \\ f(-2)=-2(-2)^2-8\\cdot(-2)-1 =7\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"387\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-48e126275f3f7f7c497b49cdf8370100_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= -1 \\ \\longrightarrow \\ f(-1)=-2(-1)^2-8\\cdot(-1)-1= 5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"386\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5a182ace189ad944ee9650df34fc695d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= -3 \\ \\longrightarrow \\ f(-3)=-2(-3)^2-8\\cdot(-3)-1= 5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"386\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-336ae2592fa21f948dc76ddb165dbf7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 0 \\ \\longrightarrow \\ f(0)=-2\\cdot0^2-8\\cdot0-1=  -1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"330\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-aafee3fbd7edddaff9f3a0f72676a3b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= -4 \\ \\longrightarrow \\ f(-4)=-2(-4)^2-8\\cdot(-4)-1= -1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"400\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\" style=\"flex-basis:33.33%\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7a2a1163e24c8a1302015eaff2bd1503_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c|c} x &amp; f(x) \\\\ \\hline -2 &amp; 7 \\\\ -1 &amp; 5 \\\\ -3 &amp; 5 \\\\ 0 &amp; -1 \\\\ -4 &amp; -1 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"134\" width=\"90\" style=\"vertical-align: -62px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Terakhir, kita plot titik-titik pada grafik dan menggambar parabola: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercice-resolu-etape-par-etape-de-la-fonction-quadratique.webp\" alt=\"latihan diselesaikan langkah demi langkah fungsi kuadrat\" class=\"wp-image-139\" width=\"281\" height=\"336\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> Latihan 5<\/h3>\n<div id=\"ezoic-pub-ad-placeholder-111\"><\/div>\n<p> Gambarlah fungsi kuadrat tidak lengkap berikut pada suatu grafik: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2e5bac9d65f6cadab9818bc92de4830f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^2+2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"106\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Lihat solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Ini adalah fungsi polinomial derajat dua. Oleh karena itu, untuk menyatakannya harus terlebih dahulu menghitung absis titik sudut parabola dengan rumus:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a07f94b2c2b30a834d1292de34ae82ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x = \\cfrac{-b}{2a} = \\cfrac{-0}{2\\cdot1} = \\cfrac{0}{2} = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"188\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dalam hal ini, fungsinya tidak lengkap karena tidak mempunyai suku derajat pertama. Untuk itu<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dad334f6e000c51bc6691844f1a7ffab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b=0 .\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"44\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang kita membuat tabel nilai. Untuk melakukan ini, kami menghitung nilai<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a7ee323bc5a3f73ad5e066b13bed5504_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"34\" style=\"vertical-align: -5px;\"><\/p>\n<p> di atas dan di sekitar atas: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-361\">\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e178a1ad103666d3b960f843389f3fce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 0 \\ \\longrightarrow \\ f(0)=0^2+2=2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"228\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-93f9a7aaa75802bd85717ec9ebdd5ed0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 1 \\ \\longrightarrow \\ f(1)=1^2+2=3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"229\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-41993cef6c11ca85064167dec57c0e9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= -1 \\ \\longrightarrow \\ f(-1)=(-1)^2+2=3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"285\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e6135721b6b23419b1fa746b6183acc8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 2 \\ \\longrightarrow \\ f(2)=2^2+2=6\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"229\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3160882279942b03e20689c0764f2135_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= -2 \\ \\longrightarrow \\ f(-2)=(-2)^2+2=6\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"285\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-71b2750173c31f2e7a31f9aeff6ac45f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c|c} x &amp; f(x) \\\\ \\hline 0 &amp; 2 \\\\ 1 &amp; 3 \\\\ -1 &amp; 3 \\\\ 2 &amp; 6 \\\\ -2 &amp; 6 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"134\" width=\"90\" style=\"vertical-align: -62px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Terakhir, kita plot titik-titik pada grafik dan menggambar parabola: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercices-resolus-pour-representer-une-fonction-quadratique-incomplete.webp\" alt=\"latihan yang diselesaikan untuk mewakili fungsi kuadrat yang tidak lengkap\" class=\"wp-image-140\" width=\"255\" height=\"285\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> Latihan 6<\/h3>\n<p> Selesaikan soal berikut yang berkaitan dengan fungsi kuadrat:<\/p>\n<p> Biaya produksi suatu produk ditentukan oleh fungsi berikut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c3e866f3ef954385f97070c37aeda9ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^2-12x+76\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"165\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Emas<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah unit yang diproduksi (dalam ribuan) dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a7ee323bc5a3f73ad5e066b13bed5504_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"34\" style=\"vertical-align: -5px;\"><\/p>\n<p> adalah biaya produksi unit (dalam ribuan euro).<\/p>\n<ul>\n<li> Mewakili fungsi biaya produksi pada grafik.<\/li>\n<li> Tentukan berapa ribu unit yang harus diproduksi untuk meminimalkan biaya. <\/li>\n<\/ul>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Lihat solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Ini adalah fungsi kuadrat. Oleh karena itu, untuk menyatakannya harus dicari terlebih dahulu absis titik puncak parabola dengan rumus:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a237afcda60e57e87029cd7bca6d4134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x = \\cfrac{-b}{2a} = \\cfrac{-(-12)}{2\\cdot 1} = \\cfrac{12}{2} = 6\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"233\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang kita membuat tabel nilai. Untuk melakukan ini, kami menghitung nilai<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a7ee323bc5a3f73ad5e066b13bed5504_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"34\" style=\"vertical-align: -5px;\"><\/p>\n<p> di atas dan di sekitar atas: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-364\">\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a354ded9ac2e79841029224a3e6d062a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 6 \\ \\longrightarrow \\ f(6)=6^2-12\\cdot6+76 = 40\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"308\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fad9733a751d03644ed384789ac0287c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 5 \\ \\longrightarrow \\ f(5)=5^2-12\\cdot5+76 = 41\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"307\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0e801ae3dc944bbd7d5638bbba43c3eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 7 \\ \\longrightarrow \\ f(7)=7^2-12\\cdot7+76 = 41\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"307\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-750d34e08cf06f200b0beb142402fbd5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 4 \\ \\longrightarrow \\ f(4)=4^2-12\\cdot4+76 =  44\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"308\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a8c9a488faf10289c77c6c79465bee25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 8 \\ \\longrightarrow \\ f(8)=8^2-12\\cdot8+76 = 44\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"308\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-aa20ac17af14b4726a38ec315091fc8d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c|c} x &amp; f(x) \\\\ \\hline 6 &amp; 40 \\\\ 5 &amp; 41 \\\\ 7 &amp; 41 \\\\ 4 &amp; 44 \\\\ 8 &amp; 44 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"134\" width=\"78\" style=\"vertical-align: -62px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Sekarang kita plot titik-titik pada grafik dan menggambar parabola: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/probleme-des-fonctions-quadratiques-ou-des-paraboles.webp\" alt=\"masalah fungsi kuadrat atau parabola\" class=\"wp-image-141\" width=\"440\" height=\"536\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> Setelah fungsinya direpresentasikan, kita akan melihat seberapa besar biaya yang diminimalkan.<\/p>\n<p class=\"has-text-align-left\"> Seperti yang ditunjukkan grafik, biaya minimum akan tercapai di puncak parabola. Karena di situlah fungsinya mengambil nilai terkecil.<\/p>\n<p class=\"has-text-align-left\"> Kesimpulannya, biaya akan diminimalkan dengan memproduksi 6.000 unit.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> Latihan 7<\/h3>\n<p> Selesaikan soal fungsi kuadrat berikut:<\/p>\n<p> Seorang atlet melakukan lempar lembing yang lintasannya dapat direpresentasikan dengan fungsi sebagai berikut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9124ad4bc986e46f99678ea39abbd596_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"h(x) = -0,025x^2+2x+2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"203\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Emas<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah meteran yang ditutupi oleh lembing dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-14b463d0ecd5b350ced6cf1d6a12eef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"h\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> tingginya (juga dalam meter).<\/p>\n<p> Berapakah tinggi maksimum yang dapat dicapai lembing tersebut? <\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Lihat solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Ini merupakan fungsi kuadrat, sehingga lintasan lembingnya berbentuk parabola.<\/p>\n<p class=\"has-text-align-left\"> Selain itu, karena koefisien suku kuadratnya negatif (-0,025), parabola akan berbentuk U terbalik dan cabang-cabangnya mengarah ke bawah. Dengan demikian lembing akan mencapai ketinggian maksimum di puncaknya, karena ini akan menjadi titik tertinggi parabola.<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu kita menghitung absis titik puncak parabola dengan rumus:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-07e71d291cd16f48045ef0f2f184fd32_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x = \\cfrac{-b}{2a} = \\cfrac{-2}{2\\cdot (-0,025)} = \\cfrac{-2}{-0,05} = 40\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"299\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Lalu kita menghitung seberapa tinggi lembing pada titik tersebut dengan mengevaluasi fungsi di dalamnya <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6a547927c07de2d21e35a28a03a13ad2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=40:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"60\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e03890524ba1ae9c5c40bc3a07f49511_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"h(40) = -0,025\\cdot (40)^2+2\\cdot 40+2 = 42\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"307\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, ketinggian maksimum yang dapat dicapai lembing adalah 42 meter.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> Latihan 8<\/h3>\n<p> Selesaikanlah soal fungsi kuadrat berikut ini:<\/p>\n<p> Biaya produksi (dalam euro) suatu perusahaan ditentukan oleh fungsi berikut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-56d12a49461c15a22fb08ddaebb62e9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C(q)=40000+20q+q^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"189\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Emas<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ac7da57d7f507262338bb5168feb3e06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"q\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: -4px;\"><\/p>\n<p> adalah unit yang diproduksi.<\/p>\n<p> Dan harga jual setiap unitnya adalah \u20ac520.<\/p>\n<ul>\n<li> Berapa keuntungan yang diperoleh perusahaan jika menjual 150 unit?<\/li>\n<li> Berapa unit yang harus dijual untuk mendapatkan keuntungan maksimal? <\/li>\n<\/ul>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Lihat solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Perusahaan memperoleh \u20ac520 untuk setiap unit yang terjual. Oleh karena itu, fungsi yang mendefinisikan pendapatan adalah:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-63d0ddca6dbabb334734ab4237be3e8b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"I(q)=520\\cdot q = 520q\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"162\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Emas<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ac7da57d7f507262338bb5168feb3e06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"q\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: -4px;\"><\/p>\n<p> adalah unit yang terjual.<\/p>\n<p class=\"has-text-align-left\"> Tapi mereka bertanya kepada kita tentang keuntungan, yaitu pendapatan dikurangi biaya. Oleh karena itu, kami mengurangkan pendapatan dikurangi biaya untuk mendapatkan fungsi yang menggambarkan laba perusahaan: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8ddf6cb21f2e6c8ff0e6f7f8bc156b7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B(q)=I(q)-C(q)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"149\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-846ac3b3a0fe227a1753a0eebc5eb5ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B(q)=520q - (40000+20q+q^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"260\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-402c374248bad2289ed95378a3a40fa1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B(q)=520q - 40000-20q-q^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"247\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6409f4ec7006749f7bcce2f9f7dab978_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B(q)=-q^2 + 500q - 40000\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"214\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Setelah kita mengetahui fungsi yang menggambarkan keuntungan perusahaan, cukup substitusikan 150 ke dalam persamaan fungsi tersebut untuk menghitung keuntungan yang diperoleh perusahaan dengan menjual 150 unit:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9f5e6f3101145bcf1a2ece4db3e07c4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} B(150) &amp; =-(150)^2 + 500\\cdot 150 - 40000 \\\\[2ex] &amp; =  -22500+75000 - 40000 \\\\[2ex] &amp; = \\bm{12500} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"100\" width=\"294\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Jadi, dengan menjual 150 unit, perusahaan akan memperoleh keuntungan sebesar \u20ac12.500.<\/p>\n<p class=\"has-text-align-left\"> Pernyataan tersebut juga meminta kita menghitung berapa unit keuntungan maksimal yang dicapai.<\/p>\n<p class=\"has-text-align-left\"> Fungsi yang menggambarkan keuntungan merupakan fungsi kuadrat, sehingga berbentuk parabola. Dan karena koefisien suku kuadratnya negatif (-1), parabola akan berbentuk U terbalik dan cabang-cabangnya mengarah ke bawah. Oleh karena itu, perolehan maksimum akan diperoleh di bagian atas, karena ini adalah titik tertinggi parabola.<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu kita menghitung absis titik puncak parabola dengan rumus:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c2a67803a02dce4f27a39a9a39319734_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x = \\cfrac{-b}{2a} = \\cfrac{-500}{2\\cdot(-1)} = \\cfrac{-500}{-2} = 250\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"273\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Jadi perusahaan akan memperoleh keuntungan maksimal dengan menjual 250 unit.<\/p>\n<p class=\"has-text-align-left\"> Sebaliknya, meski siaran pers tidak menanyakannya, kita bisa menentukan keuntungan yang didapat dengan menjual 250 unit ini:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2823628ca7484d5baaa4e1b7b003cc41_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B(250) =-(250)^2 + 500\\cdot250- 40000= 22500\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"362\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u20ac <\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<p><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-109\"><strong> <\/strong><\/div>\n<p><strong><br \/><\/strong><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Halaman ini menjelaskan apa itu fungsi kuadrat beserta seluruh ciri-cirinya: kelengkungan, titik sudut, titik potong dengan sumbu, dll. Anda juga akan mempelajari cara merepresentasikan fungsi kuadrat pada grafik. Dan terakhir, Anda dapat berlatih dengan contoh, latihan langkah demi langkah, dan soal fungsi kuadrat. Apa itu fungsi kuadrat? Pengertian fungsi kuadrat adalah sebagai berikut: Dalam matematika, &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/fungsi-parabola-kuadrat\/\"> <span class=\"screen-reader-text\">Fungsi kuadrat atau parabola<\/span> Selengkapnya &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[49],"tags":[],"class_list":["post-7","post","type-post","status-publish","format-standard","hentry","category-representasi-fungsi"],"yoast_head":"<!-- This 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