{"id":356,"date":"2023-07-04T22:26:55","date_gmt":"2023-07-04T22:26:55","guid":{"rendered":"https:\/\/mathority.org\/id\/fungsi-interpolasi-linier-dan-kuadrat\/"},"modified":"2023-07-04T22:26:55","modified_gmt":"2023-07-04T22:26:55","slug":"fungsi-interpolasi-linier-dan-kuadrat","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/fungsi-interpolasi-linier-dan-kuadrat\/","title":{"rendered":"Interpolasi linier dan kuadrat"},"content":{"rendered":"<p>Di halaman ini Anda akan mempelajari apa yang dimaksud dengan interpolasi suatu fungsi. Secara khusus dijelaskan interpolasi linier dan interpolasi kuadrat. Selain itu, Anda akan dapat melihat banyak contoh sehingga Anda tidak ragu tentang bagaimana suatu fungsi diinterpolasi. <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-104\"><\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-interpolacion-de-una-funcion\"><\/span> Apa itu interpolasi fungsi?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Pengertian interpolasi adalah sebagai berikut: <\/p>\n<div style=\"background:linear-gradient(to bottom, #FFFFFF 0%, #FFE0B2 100%); 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>interpolasi<\/strong> adalah prosedur yang digunakan untuk memperkirakan nilai suatu fungsi pada suatu titik pada interval yang titik akhirnya diketahui. <\/p>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcual-es-la-diferencia-entre-la-interpolacion-y-la-extrapolacion\"><\/span> Apa perbedaan antara interpolasi dan ekstrapolasi? <span class=\"ez-toc-section-end\"><\/span><\/h2>\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>Interpolasi dan ekstrapolasi memiliki arti yang sangat mirip, karena keduanya melibatkan estimasi nilai suatu fungsi pada suatu titik dari dua titik yang diketahui.<\/p>\n<p> Namun, interpolasi terdiri dari membuat perkiraan suatu titik yang terletak pada interval yang dibentuk oleh dua titik yang diketahui tersebut. Sebaliknya, mengekstrapolasi berarti memperkirakan nilai fungsi pada suatu titik di luar interval yang terdiri dari dua titik yang diketahui tersebut. <\/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\/interpolation-et-extrapolation-ou-interpoler-extrapoler.webp\" alt=\"interpolasi dan ekstrapolasi atau interpolasi dan ekstrapolasi\" class=\"wp-image-114\" width=\"370\" height=\"294\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Seperti terlihat pada grafik di atas, titik-titik yang diketahui adalah (2,3) dan (6,5). Dalam hal ini, kita ingin melakukan interpolasi ke x=4, karena berada di antara titik-titik yang diketahui, dan sebaliknya, kita ingin melakukan ekstrapolasi ke x=8, karena berada di luar interval yang diketahui.<\/p>\n<p> Jelasnya, nilai yang diinterpolasi jauh lebih dapat diandalkan daripada nilai yang diekstrapolasi, karena dalam ekstrapolasi kita berasumsi bahwa fungsi tersebut akan mengikuti jalur yang sama. Namun, ada kemungkinan kemiringan fungsi berubah di luar batas interval yang diketahui dan pendugaannya salah.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"interpolacion-lineal\"><\/span> Interpolasi linier<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Interpolasi linier adalah kasus khusus interpolasi polinomial Newton. Dalam hal ini digunakan polinomial derajat pertama, yaitu fungsi linier atau affine, untuk menebak nilai fungsi di suatu titik. <\/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\"> Mengingat dua poin yang diketahui,<\/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-99906702500e51b12e2859cc804a7b57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_1(x_1,y_1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -5px;\"><\/p>\n<p> Dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4b79aabad6138add43cc540b4205d672_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_2(x_2,y_2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -5px;\"><\/p>\n<p> , rumus untuk melakukan interpolasi linier 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-6f47466bf8293e2bb88ede2994c7b2ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\cfrac{y_2-y_1}{x_2-x_1}\\cdot(x-x_1) + y_1\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"205\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<p style=\"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-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> Dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> adalah koordinat titik yang diinterpolasi.<\/p>\n<\/div>\n<p> Kita dapat memverifikasi bahwa rumus ini sesuai dengan persamaan titik-kemiringan garis. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-interpolar-linealmente\"><\/span> Contoh interpolasi linier <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><meta charset=\"utf-8\"><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-106\"><\/div>\n<\/div>\n<p> Selanjutnya kita akan melihat soal sebagai contoh untuk menyelesaikan pemahaman konsep interpolasi linier:<\/p>\n<ul>\n<li> Dalam sebuah pabrik, 2 barang diproduksi dalam waktu 4 jam dan 10 barang dalam waktu 8 jam. Jika jumlah barang yang diproduksi mempunyai hubungan linier dengan jam kerja, berapa banyak barang yang akan diproduksi dalam 5 jam?<\/li>\n<\/ul>\n<p> Pertama, kita perlu mendefinisikan fungsi linier yang menghubungkan jam kerja dengan barang yang diproduksi. Dalam hal ini, X adalah jam kerja dan Y adalah barang yang diproduksi. Karena banyak atau sedikitnya barang yang diproduksi bergantung pada jam kerja, atau dengan kata lain produksi bergantung pada jam, bukan sebaliknya.<\/p>\n<p> Dari pernyataan tersebut kita mengetahui bahwa fungsi tersebut melalui titik (4,2) dan (8,10). Oleh karena itu, cukup menerapkan rumus untuk melakukan interpolasi 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-c60268650a59ab9a9a60303fd1414aa3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=5:\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"52\" 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-6f47466bf8293e2bb88ede2994c7b2ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\cfrac{y_2-y_1}{x_2-x_1}\\cdot(x-x_1) + y_1\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"205\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<p> Kami mengganti nilai poin ke dalam persamaan:<\/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-def761f7a698a9bc301b289bada81411_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\cfrac{10-2}{8-4}\\cdot(5-4) + 2\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"179\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Dan kami melakukan operasi:<\/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-c5106bdb787f68d2f725eeb48e11eee1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\cfrac{8}{4}\\cdot1 + 2 = 2\\cdot 1 +2 = 4\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"213\" 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-282fa83a6377c6833872c037158e74f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{y=4}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Jadi 5 jam akan menghasilkan <strong>4 item<\/strong> .<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"interpolacion-cuadratica\"><\/span> interpolasi kuadrat<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Interpolasi kuadrat melibatkan interpolasi dengan polinomial derajat kedua, bukan polinomial derajat 1. Oleh karena itu, dalam kasus ini, digunakan fungsi <strong>kuadrat<\/strong> atau <strong>parabola<\/strong> .<\/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-f269c04d9aa0012a945df0050a50c90e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y = ax^2+bx+c\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"129\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Secara umum interpolasi orde kedua lebih akurat dibandingkan interpolasi orde pertama karena derajatnya lebih tinggi. Sebaliknya, diperlukan satu titik lagi untuk dapat melakukan interpolasi.<\/p>\n<p> Ahli matematika <a href=\"https:\/\/www.ugr.es\/~eaznar\/lagrange.htm\" target=\"_blank\" rel=\"noreferrer noopener\">Lagrange<\/a> mengembangkan rumus untuk mencari fungsi interpolasi orde n. Untuk kasus orde kedua, <strong>polinomial interpolasi Lagrange<\/strong> adalah 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-7964f224af5150a7765843814e8e2cc2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\cfrac{(x-x_1)(x-x_2)}{(x_0-x_1)(x-x_2)}\\cdot y_0+ \\cfrac{(x-x_0)(x-x_2)}{(x_1-x_0)(x_0-x_2)}\\cdot y_1+ \\cfrac{(x-x_0)(x-x_1)}{(x_2-x_0)(x_2-x_1)}\\cdot y_2\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"588\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> dimana titik-titik yang diketahui<\/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-99906702500e51b12e2859cc804a7b57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_1(x_1,y_1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -5px;\"><\/p>\n<p> ,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4b79aabad6138add43cc540b4205d672_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_2(x_2,y_2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -5px;\"><\/p>\n<p> Dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dac17428ab0a8569f50aacbb6e002ca8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_3(x_3,y_3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -5px;\"><\/p>\n<p> Mereka digunakan untuk mencari nilai fungsi pada absis<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a9cc293b28f198c32e0356b52e2e23bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Namun dalam praktiknya, metode interpolasi Lagrange umumnya tidak digunakan, melainkan fungsi kuadrat dihitung dari 3 titik yang diamati, kemudian titik yang akan diinterpolasi dalam fungsi tersebut dievaluasi. Berikut adalah latihan yang diselesaikan untuk melihat cara melakukannya: <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-interpolar-cuadraticamente\"><\/span> Contoh interpolasi kuadrat <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><meta charset=\"utf-8\"><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-107\"><\/div>\n<\/div>\n<ul>\n<li> Tentukan fungsi kuadrat yang melalui titik (0,1), (1,0) dan (3,4) kemudian interpolasi nilai\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6de4e73609a66312d9714a253f9ae3a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=-1.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"61\" style=\"vertical-align: 0px;\"><\/p>\n<\/li>\n<\/ul>\n<p> Karena fungsi kuadrat adalah polinomial orde dua, fungsi interpolasinya adalah 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-f269c04d9aa0012a945df0050a50c90e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y = ax^2+bx+c\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"129\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, perlu untuk menghitung koefisiennya<\/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-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> ,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> Dan<\/p>\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> . Untuk melakukan ini, kita substitusikan koordinat titik-titik yang diketahui ke dalam fungsi:<\/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-688e308fcaa3e4187058fb9145b6406a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left.\\begin{array}{l} 1 = a\\cdot 0^2+b\\cdot 0+c \\\\[2ex] 0 = a\\cdot 1^2+b\\cdot 1+c \\\\[2ex] 4 = a\\cdot 3^2+b\\cdot 3+c \\end{array} \\right\\} \\longrightarrow \\left.\\begin{array}{l} 1 = c \\\\[2ex] 0 = a+b+c \\\\[2ex] 4 = 9a+3b+c \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"363\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Kami sekarang memecahkan sistem persamaan:<\/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-671f07a2311e3f14886d400a1418e3b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left.\\begin{array}{l} 1 = c \\\\[2ex] 0 = a+b+c \\\\[2ex] 4 = 9a+3b+c \\end{array} \\right\\} \\begin{array}{l} \\\\[2ex] \\xrightarrow{c \\ = \\ 1} \\\\[2ex] &amp; \\end{array} \\left.\\begin{array}{l} c=1 \\\\[2ex] 0 = a+b+1 \\\\[2ex] 4 = 9a+3b+1 \\end{array}\\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"96\" width=\"361\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Kita sudah mengetahui nilai dari<\/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-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> , oleh karena itu kita dapat menyelesaikan sistem tersebut dengan metode substitusi: kita menghapus yang tidak diketahui<\/p>\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> dari persamaan kedua dan substitusikan ekspresi yang ditemukan pada persamaan terakhir:<\/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-0be4db125be3270895ed6c2788990724_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left.\\begin{array}{l} a=-b-1 \\\\[2ex]  4 = 9a+3b+1 \\end{array}\\right\\}\\longrightarrow \\left.\\begin{array}{l} a=-b-1 \\\\[2ex] 4 = 9(-b-1)+3b+1 \\end{array}\\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"389\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> kita menemukan hal yang tidak diketahui<\/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-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> dari persamaan terakhir: <\/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-00a4283dc06626da922a6a85a95139ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4 = -9b-9+3b+1\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"161\" style=\"vertical-align: -2px;\"><\/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-258e9e8665683efd2a410bcf9954055c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"12 =-6b\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"71\" 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-7efb512d185829bbfa278f182d5a8cfb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b=\\cfrac{12}{-6} = -2\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"101\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> dan carilah nilai dari<\/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-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> dengan persamaan kedua sistem:<\/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-0f22f34c05dfd7e8801920f909d975e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a=-(-2)-1 = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"145\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, fungsi kuadratnya adalah 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-e8967d1bbbab2f2d3b4be41d78bbefe1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{y = x^2-2x+1}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"121\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Terakhir, kami menginterpolasi absisnya<\/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-ad143a0d979362a51b48a48c9ca9f59e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=-1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" style=\"vertical-align: 0px;\"><\/p>\n<p> untuk menghitung nilai fungsi pada titik 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-03ef4ea569c4913d354adeb167adf063_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=(-1)^2-2\\cdot(-1)+1=1+2+1=\\bm{4}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"314\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p><meta charset=\"utf-8\"><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-108\"><\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"aplicaciones-de-la-interpolacion\"><\/span> Aplikasi Interpolasi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Meskipun kelihatannya tidak demikian, interpolasi sangat berguna dalam matematika dan statistik. Misalnya, digunakan untuk mencoba memprediksi nilai suatu fungsi: dari serangkaian data yang dikumpulkan, garis regresi dihitung dan dengan itu Anda dapat memperkirakan nilai fungsi tersebut di setiap titik.<\/p>\n<p> Interpolasi suatu fungsi dapat dilakukan secara manual, seperti yang telah kita lihat, atau dengan program komputer seperti Excel atau MATLAB. Tentu saja, jauh lebih nyaman dan cepat melakukan hal ini dengan menggunakan komputer.<\/p>\n<p> Di sisi lain, interpolasi juga digunakan untuk menyederhanakan perhitungan. Ada beberapa program perangkat lunak yang perlu melakukan penghitungan kompleks dengan fungsi yang sangat panjang, jadi terkadang interpolasi linier dari fungsi ini dilakukan untuk menyederhanakan pengoperasian. <\/p>\n<p><meta charset=\"utf-8\"><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-109\"><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Di halaman ini Anda akan mempelajari apa yang dimaksud dengan interpolasi suatu fungsi. Secara khusus dijelaskan interpolasi linier dan interpolasi kuadrat. Selain itu, Anda akan dapat melihat banyak contoh sehingga Anda tidak ragu tentang bagaimana suatu fungsi diinterpolasi. Apa itu interpolasi fungsi? Pengertian interpolasi adalah sebagai berikut: Dalam matematika, interpolasi adalah prosedur yang digunakan untuk &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/fungsi-interpolasi-linier-dan-kuadrat\/\"> <span class=\"screen-reader-text\">Interpolasi linier dan kuadrat<\/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-356","post","type-post","status-publish","format-standard","hentry","category-representasi-fungsi"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Interpolasi linier dan kuadrat - Mathority<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/id\/fungsi-interpolasi-linier-dan-kuadrat\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Interpolasi linier dan kuadrat - Mathority\" \/>\n<meta property=\"og:description\" content=\"Di halaman ini Anda akan mempelajari apa yang dimaksud dengan interpolasi suatu fungsi. Secara khusus dijelaskan interpolasi linier dan interpolasi kuadrat. Selain itu, Anda akan dapat melihat banyak contoh sehingga Anda tidak ragu tentang bagaimana suatu fungsi diinterpolasi. Apa itu interpolasi fungsi? 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