{"id":11038,"date":"2015-07-14T17:55:50","date_gmt":"2015-07-14T17:55:50","guid":{"rendered":"https:\/\/courses.candelalearning.com\/osprecalc\/?post_type=chapter&#038;p=11038"},"modified":"2015-09-04T21:03:16","modified_gmt":"2015-09-04T21:03:16","slug":"key-concepts-glossary-8","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/chapter\/key-concepts-glossary-8\/","title":{"raw":"Key Concepts &amp; Glossary","rendered":"Key Concepts &amp; Glossary"},"content":{"raw":"<section id=\"fs-id1165134205927\" class=\"key-equations\" data-depth=\"1\">\r\n<h2 data-type=\"title\">Key Equations<\/h2>\r\n<table id=\"eip-id1165137539373\" summary=\"..\">\r\n<tbody>\r\n<tr>\r\n<td data-valign=\"middle\" data-align=\"left\">general form of a quadratic function<\/td>\r\n<td>[latex]f\\left(x\\right)=a{x}^{2}+bx+c[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-valign=\"middle\" data-align=\"left\">the quadratic formula<\/td>\r\n<td>[latex]x=\\frac{-b\\pm \\sqrt{{b}^{2}-4ac}}{2a}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-valign=\"middle\" data-align=\"left\">standard form of a quadratic function<\/td>\r\n<td>[latex]f\\left(x\\right)=a{\\left(x-h\\right)}^{2}+k[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/section><section id=\"fs-id1165135426424\" class=\"key-concepts\" data-depth=\"1\">\r\n<h2 data-type=\"title\">Key Concepts<\/h2>\r\n<ul id=\"fs-id1165134570662\">\r\n\t<li>A polynomial function of degree two is called a quadratic function.<\/li>\r\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>\r\n\t<li>The axis of symmetry is the vertical line passing through the vertex. The zeros, or <em>x<\/em>-intercepts, are the points at which the parabola crosses the <em>x<\/em>-axis. The <em>y<\/em>-intercept is the point at which the parabola crosses the <em>y-<\/em>axis.<\/li>\r\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>\r\n\t<li>The vertex can be found from an equation representing a quadratic function.<\/li>\r\n\t<li>The domain of a quadratic function is all real numbers. The range varies with the function.<\/li>\r\n\t<li>A quadratic function\u2019s minimum or maximum value is given by the <em>y<\/em>-value of the vertex.<\/li>\r\n\t<li>The minimum or maximum value of a quadratic function can be used to determine the range of the function and to solve many kinds of real-world problems, including problems involving area and revenue.<\/li>\r\n\t<li>Some quadratic equations must be solved by using the quadratic formula.<\/li>\r\n\t<li>The vertex and the intercepts can be identified and interpreted to solve real-world problems.<\/li>\r\n<\/ul>\r\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\r\n<dl id=\"fs-id1165135449657\" class=\"definition\"><dt><strong>axis of symmetry<\/strong><\/dt><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><\/dl><dl id=\"fs-id1165135502777\" class=\"definition\"><dt><strong>general form of a quadratic function<\/strong><\/dt><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 <em>a<\/em>,\u00a0<em>b<\/em>, and\u00a0<em>c<\/em>\u00a0are real numbers and [latex]a\\ne 0[\/latex].<\/dd><\/dl><dl id=\"fs-id1165137931314\" class=\"definition\"><dt><strong>standard form of a quadratic function<\/strong><\/dt><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><\/dl><dl id=\"fs-id1165135623614\" class=\"definition\"><dt><strong>vertex<\/strong><\/dt><dd id=\"fs-id1165135623619\">the point at which a parabola changes direction, corresponding to the minimum or maximum value of the quadratic function<\/dd><\/dl><dl id=\"fs-id1165135623624\" class=\"definition\"><dt><strong>vertex form of a quadratic function<\/strong><\/dt><dd id=\"fs-id1165135623630\">another name for the standard form of a quadratic function<\/dd><\/dl><dl id=\"fs-id1165135623634\" class=\"definition\"><dt><strong>zeros<\/strong><\/dt><dd id=\"fs-id1165135623639\">in a given function, the values of <em>x<\/em>\u00a0at which <em>y<\/em> = 0, also called roots<\/dd><\/dl><\/section>","rendered":"<section id=\"fs-id1165134205927\" class=\"key-equations\" data-depth=\"1\">\n<h2 data-type=\"title\">Key Equations<\/h2>\n<table id=\"eip-id1165137539373\" summary=\"..\">\n<tbody>\n<tr>\n<td data-valign=\"middle\" data-align=\"left\">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 data-valign=\"middle\" data-align=\"left\">the quadratic formula<\/td>\n<td>[latex]x=\\frac{-b\\pm \\sqrt{{b}^{2}-4ac}}{2a}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td data-valign=\"middle\" data-align=\"left\">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\" data-depth=\"1\">\n<h2 data-type=\"title\">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. The zeros, or <em>x<\/em>-intercepts, are the points at which the parabola crosses the <em>x<\/em>-axis. The <em>y<\/em>-intercept is the point at which the parabola crosses the <em>y-<\/em>axis.<\/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<li>A quadratic function\u2019s minimum or maximum value is given by the <em>y<\/em>-value of the vertex.<\/li>\n<li>The minimum or maximum value of a quadratic function can be used to determine the range of the function and to solve many kinds of real-world problems, including problems involving area and revenue.<\/li>\n<li>Some quadratic equations must be solved by using the quadratic formula.<\/li>\n<li>The vertex and the intercepts can be identified and interpreted to solve real-world problems.<\/li>\n<\/ul>\n<h2 data-type=\"glossary-title\">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 <em>a<\/em>,\u00a0<em>b<\/em>, and\u00a0<em>c<\/em>\u00a0are 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><strong>vertex<\/strong><\/dt>\n<dd id=\"fs-id1165135623619\">the point at which a parabola changes direction, corresponding to the minimum or maximum value of the quadratic function<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135623624\" class=\"definition\">\n<dt><strong>vertex form of a quadratic function<\/strong><\/dt>\n<dd id=\"fs-id1165135623630\">another name for the standard form of a quadratic function<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135623634\" class=\"definition\">\n<dt><strong>zeros<\/strong><\/dt>\n<dd id=\"fs-id1165135623639\">in a given function, the values of <em>x<\/em>\u00a0at which <em>y<\/em> = 0, also called roots<\/dd>\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-11038\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Precalculus. <strong>Authored by<\/strong>: Jay Abramson, et al.. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175\">http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175<\/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\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175.<\/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":276,"menu_order":6,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Precalculus\",\"author\":\"Jay Abramson, et al.\",\"organization\":\"OpenStax\",\"url\":\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download For Free at : http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175.\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-11038","chapter","type-chapter","status-publish","hentry"],"part":11026,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/pressbooks\/v2\/chapters\/11038","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/wp\/v2\/users\/276"}],"version-history":[{"count":5,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/pressbooks\/v2\/chapters\/11038\/revisions"}],"predecessor-version":[{"id":12781,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/pressbooks\/v2\/chapters\/11038\/revisions\/12781"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/pressbooks\/v2\/parts\/11026"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/pressbooks\/v2\/chapters\/11038\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/wp\/v2\/media?parent=11038"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/pressbooks\/v2\/chapter-type?post=11038"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/wp\/v2\/contributor?post=11038"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/wp\/v2\/license?post=11038"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}