{"id":154142,"date":"2022-03-25T23:12:23","date_gmt":"2022-03-25T17:42:23","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/polynomial-function-definition-examples-types-graphs-and-examples\/"},"modified":"2022-12-27T14:54:21","modified_gmt":"2022-12-27T09:24:21","slug":"polynomial-function-definition-examples-types-graphs-and-examples","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/polynomial-function\/","title":{"rendered":"Polynomial Function &#8211; Definition, Examples, Types, Graphs and Examples"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/polynomial-function\/#What_is_a_Polynomial_Function\" title=\"What is a Polynomial Function?\">What is a Polynomial Function?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/polynomial-function\/#Polynomial_Function_Definition\" title=\"Polynomial Function Definition\">Polynomial Function Definition<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/polynomial-function\/#Polynomial_Function_Examples\" title=\"Polynomial Function Examples\">Polynomial Function Examples<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/polynomial-function\/#Types_of_Polynomial_Function\" title=\"Types of Polynomial Function\">Types of Polynomial Function<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/polynomial-function\/#Graphs_of_Polynomial_Function\" title=\"Graphs of Polynomial Function\">Graphs of Polynomial Function<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/polynomial-function\/#Quadratic_Polynomial_Function\" title=\"Quadratic Polynomial Function\">Quadratic Polynomial Function<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/polynomial-function\/#Graph_of_High_Degree_Polynomial_Function\" title=\"Graph of High Degree Polynomial Function\">Graph of High Degree Polynomial Function<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"What_is_a_Polynomial_Function\"><\/span>What is a Polynomial Function?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Polynomial Function &#8211; Definition: A <a href=\"https:\/\/infinitylearn.com\/surge\/maths\/polynomial-function\/\">polynomial function<\/a> is a mathematical function that can be expressed as a sum of terms, each of which is a monomial multiplied by a coefficient. In other words, a polynomial function is a function that can be written in the form:<\/p>\n<p>f(x) = a 0 xn + a 1 xn-1 + a 2 xn-2 + &#8230; + a n-1 x + a n<\/p>\n<p>where a 0 , a 1 , a 2 , &#8230;, a n are real numbers and n is a positive integer.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-154141 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/polynomial-function-definition-examples-types-graphs-and-examples.jpg\" alt=\"Polynomial Function - Definition, Examples, Types, Graphs and Examples\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/polynomial-function-definition-examples-types-graphs-and-examples.jpg?v=1648230138 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/polynomial-function-definition-examples-types-graphs-and-examples-300x212.jpg?v=1648230138 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Polynomial_Function_Definition\"><\/span>Polynomial Function Definition<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A polynomial function is a mathematical function that can represented by a sum of terms, each of which is a product of a number (the coefficient) and a power of x (the variable). The degree of a polynomial is the largest power of x in any of its terms. Polynomial functions are used to model a wide variety of real-world situations.<\/p>\n<p>A polynomial function can written in standard form, using the variable x, the degree of the polynomial, and the coefficients of the terms in descending order of power:<\/p>\n<p>f(x) = a 0 xn + a 1 xn-1 + a 2 xn-2 + &#8230; + a n-1 x + a n<\/p>\n<p>where a 0 is the coefficient of the x0 term, a 1 is the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Coefficient\">coefficient <\/a>of the x1 term, and so on.<\/p>\n<p>Polynomial functions can also written in factored form, using the factors of the polynomials greatest common divisor (GCD). The GCD is the largest number that divides evenly into all the terms of the polynomial. The factors of the GCD are the polynomial&#8217;s roots, or solutions. In factored form, a polynomial function can written as:<\/p>\n<p>f(x) = (x \u2212 r 1 )(x \u2212 r 2 )(x \u2212 r 3 ) &#8230; (x \u2212 r n )<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Polynomial_Function_Examples\"><\/span>Polynomial Function Examples<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A polynomial is a mathematical function that can written in the form:<\/p>\n<p>f(x) = a n xn + a n-1 xn-1 + &#8230; + a 1 x + a 0<\/p>\n<p>Where a 0 , a 1 , a 2 , &#8230;, a n are real numbers and x is a real variable.<\/p>\n<p>Polynomials can used to model a wide variety of situations. Some examples include:<\/p>\n<ul>\n<li>The height, h(t), of a ball thrown into the air at time, t<\/li>\n<li>The temperature, T(x), of a room as a function of time, x<\/li>\n<li>The cost, C(x), of producing x units of a product<\/li>\n<\/ul>\n<p>All of these situations can represented by polynomial functions.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Types_of_Polynomial_Function\"><\/span>Types of Polynomial Function<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>There are three types of polynomial function: linear, quadratic, and cubic.<\/p>\n<p>Linear Polynomial: A linear polynomial is a polynomial with degree one. The equation of a linear polynomial is y = ax + b, where a and b are constants.<\/p>\n<p>Quadratic Polynomial: A quadratic polynomial is a polynomial with degree two. The equation of a quadratic polynomial is y = ax2 + bx + c, where a, b, and c are constants.<\/p>\n<p>Cubic Polynomial: A cubic polynomial is a polynomial with degree three. The equation of a cubic polynomial is y = ax3 + bx2 + cx + d, where a, b, c, and d are constants.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Graphs_of_Polynomial_Function\"><\/span>Graphs of Polynomial Function<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The graphs of polynomial functions are continuous and smooth. They typically rise and then level off as they near infinity. The shapes of their graphs depend on the degree of the polynomial function. Higher degree polynomial functions have more complex shapes.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Quadratic_Polynomial_Function\"><\/span>Quadratic Polynomial Function<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A quadratic polynomial function is a function that can represented by a polynomial equation of the form<\/p>\n<p>where &#8220;a&#8221;, &#8220;b&#8221;, and &#8220;c&#8221; are real numbers and &#8220;x&#8221; is a real number. The graph of a quadratic polynomial function is a parabola.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Graph_of_High_Degree_Polynomial_Function\"><\/span>Graph of High Degree Polynomial Function<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>This graph of a high degree polynomial function shows the general shape of the curve. As the degree of the polynomial increases, the curve becomes more and more curved.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is a Polynomial Function? Polynomial Function &#8211; Definition: A polynomial function is a mathematical function that can be expressed [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Polynomial Function - Definition","_yoast_wpseo_title":"%%title%% %%page%%","_yoast_wpseo_metadesc":"Learn about Polynomial Function topic of Maths in details explained by subject experts on infinitylearn.com. 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