{"id":195,"date":"2023-06-21T13:22:42","date_gmt":"2023-06-21T13:22:42","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/summary-quadratic-functions\/"},"modified":"2023-07-03T20:20:43","modified_gmt":"2023-07-03T20:20:43","slug":"summary-quadratic-functions","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/summary-quadratic-functions\/","title":{"raw":"Summary: Graphs of Quadratic Functions","rendered":"Summary: Graphs of Quadratic Functions"},"content":{"raw":"\n\n<section id=\"fs-id1165134205927\" class=\"key-equations\">\n<h2>Key Equations<\/h2>\n<table id=\"eip-id1165137539373\" summary=\"..\">\n<tbody>\n<tr>\n<td>general form of a quadratic function<\/td>\n<td>[latex]f\\left(x\\right)=a{x}^{2}+bx+c[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>standard form of a quadratic function<\/td>\n<td>[latex]f\\left(x\\right)=a{\\left(x-h\\right)}^{2}+k[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/section><section id=\"fs-id1165135426424\" class=\"key-concepts\">\n<h2>Key Concepts<\/h2>\n<ul id=\"fs-id1165134570662\">\n \t<li>A polynomial function of degree two is called a quadratic function.<\/li>\n \t<li>The graph of a quadratic function is a parabola. A parabola is a U-shaped curve that can open either up or down.<\/li>\n \t<li>The axis of symmetry is the vertical line passing through the vertex.<\/li>\n \t<li>Quadratic functions are often written in general form. Standard or vertex form is useful to easily identify the vertex of a parabola. Either form can be written from a graph.<\/li>\n \t<li>The vertex can be found from an equation representing a quadratic function.<\/li>\n \t<li>The domain of a quadratic function is all real numbers. The range varies with the function.<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<dl id=\"fs-id1165135449657\" class=\"definition\">\n \t<dt><strong>axis of symmetry<\/strong><\/dt>\n \t<dd id=\"fs-id1165135449662\">a vertical line drawn through the vertex of a parabola around which the parabola is symmetric; it is defined by [latex]x=-\\frac{b}{2a}[\/latex].<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135502777\" class=\"definition\">\n \t<dt><strong>general form of a quadratic function<\/strong><\/dt>\n \t<dd id=\"fs-id1165135502783\">the function that describes a parabola, written in the form [latex]f\\left(x\\right)=a{x}^{2}+bx+c[\/latex], where [latex]a[\/latex], [latex]b[\/latex], and [latex]c[\/latex]&nbsp;are real numbers and [latex]a\\ne 0[\/latex].<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137931314\" class=\"definition\">\n \t<dt><strong>standard form of a quadratic function<\/strong><\/dt>\n \t<dd id=\"fs-id1165137931319\">the function that describes a parabola, written in the form [latex]f\\left(x\\right)=a{\\left(x-h\\right)}^{2}+k[\/latex], where [latex]\\left(h,\\text{ }k\\right)[\/latex] is the vertex.<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135623614\" class=\"definition\">\n \t<dt><\/dt>\n<\/dl>\n<\/section>\n\n","rendered":"<section id=\"fs-id1165134205927\" class=\"key-equations\">\n<h2>Key Equations<\/h2>\n<table id=\"eip-id1165137539373\" summary=\"..\">\n<tbody>\n<tr>\n<td>general form of a quadratic function<\/td>\n<td>[latex]f\\left(x\\right)=a{x}^{2}+bx+c[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>standard form of a quadratic function<\/td>\n<td>[latex]f\\left(x\\right)=a{\\left(x-h\\right)}^{2}+k[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/section>\n<section id=\"fs-id1165135426424\" class=\"key-concepts\">\n<h2>Key Concepts<\/h2>\n<ul id=\"fs-id1165134570662\">\n<li>A polynomial function of degree two is called a quadratic function.<\/li>\n<li>The graph of a quadratic function is a parabola. A parabola is a U-shaped curve that can open either up or down.<\/li>\n<li>The axis of symmetry is the vertical line passing through the vertex.<\/li>\n<li>Quadratic functions are often written in general form. Standard or vertex form is useful to easily identify the vertex of a parabola. Either form can be written from a graph.<\/li>\n<li>The vertex can be found from an equation representing a quadratic function.<\/li>\n<li>The domain of a quadratic function is all real numbers. The range varies with the function.<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<dl id=\"fs-id1165135449657\" class=\"definition\">\n<dt><strong>axis of symmetry<\/strong><\/dt>\n<dd id=\"fs-id1165135449662\">a vertical line drawn through the vertex of a parabola around which the parabola is symmetric; it is defined by [latex]x=-\\frac{b}{2a}[\/latex].<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135502777\" class=\"definition\">\n<dt><strong>general form of a quadratic function<\/strong><\/dt>\n<dd id=\"fs-id1165135502783\">the function that describes a parabola, written in the form [latex]f\\left(x\\right)=a{x}^{2}+bx+c[\/latex], where [latex]a[\/latex], [latex]b[\/latex], and [latex]c[\/latex]&nbsp;are real numbers and [latex]a\\ne 0[\/latex].<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137931314\" class=\"definition\">\n<dt><strong>standard form of a quadratic function<\/strong><\/dt>\n<dd id=\"fs-id1165137931319\">the function that describes a parabola, written in the form [latex]f\\left(x\\right)=a{\\left(x-h\\right)}^{2}+k[\/latex], where [latex]\\left(h,\\text{ }k\\right)[\/latex] is the vertex.<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135623614\" class=\"definition\">\n<dt><\/dt>\n<\/dl>\n<\/section>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-195\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Revision and Adaptation. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>College Algebra. <strong>Authored by<\/strong>: Abramson, Jay et al.. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2\">http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":395986,"menu_order":32,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"College Algebra\",\"author\":\"Abramson, Jay et 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