{"id":186,"date":"2023-06-21T13:22:41","date_gmt":"2023-06-21T13:22:41","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/summary-review-17\/"},"modified":"2023-07-03T20:00:58","modified_gmt":"2023-07-03T20:00:58","slug":"summary-review-17","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/summary-review-17\/","title":{"raw":"Summary: Review","rendered":"Summary: Review"},"content":{"raw":"\n\nKey Concepts\n<ul>\n \t<li>Quadratic functions of form [latex]f(x)=ax^2+bx+c[\/latex] may be graphed by evaluating the function at various values of the input variable [latex]x[\/latex] to find each coordinating output [latex]f(x)[\/latex]. Plot enough points to obtain the shape of the graph, then draw a smooth curve between them.<\/li>\n \t<li>The vertex (the turning point) of the graph of a parabola may be obtained using the formula [latex]\\left( -\\dfrac{b}{2a}, f\\left(-\\dfrac{b}{2a}\\right)\\right)[\/latex]<\/li>\n \t<li>The graph of a quadratic function opens up if the leading coefficient [latex]a[\/latex] is positive, and opens down if [latex]a[\/latex] is negative.<\/li>\n        <li>Quadratic functions may be used to model various real-life situations such as projectile motion, and used to determine inputs required to maximize or minimize certain outputs in cost or revenue models.<\/li>\n \t\n<\/ul>\n<h2>Glossary<\/h2>\n<dl>\n        <dt><strong>projectile motion<\/strong><\/dt>\n \t<dd>(also called parabolic trajectory) a projectile launched or thrown into the air will follow a curved path in the shape of a parabola<\/dd>\n \t<dt><strong>quadratic function<\/strong><\/dt>\n \t<dd>a function of form [latex]f(x)=ax^2+bx+c[\/latex] whose graph forms a parabola in the real plane<\/dd>\n \t<dt><strong>vertex<\/strong><\/dt>\n \t<dd>the turning point of the graph of quadratic function<\/dd>\n \t\n \t\n<\/dl>\n\n\n","rendered":"<p>Key Concepts<\/p>\n<ul>\n<li>Quadratic functions of form [latex]f(x)=ax^2+bx+c[\/latex] may be graphed by evaluating the function at various values of the input variable [latex]x[\/latex] to find each coordinating output [latex]f(x)[\/latex]. Plot enough points to obtain the shape of the graph, then draw a smooth curve between them.<\/li>\n<li>The vertex (the turning point) of the graph of a parabola may be obtained using the formula [latex]\\left( -\\dfrac{b}{2a}, f\\left(-\\dfrac{b}{2a}\\right)\\right)[\/latex]<\/li>\n<li>The graph of a quadratic function opens up if the leading coefficient [latex]a[\/latex] is positive, and opens down if [latex]a[\/latex] is negative.<\/li>\n<li>Quadratic functions may be used to model various real-life situations such as projectile motion, and used to determine inputs required to maximize or minimize certain outputs in cost or revenue models.<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<dl>\n<dt><strong>projectile motion<\/strong><\/dt>\n<dd>(also called parabolic trajectory) a projectile launched or thrown into the air will follow a curved path in the shape of a parabola<\/dd>\n<dt><strong>quadratic function<\/strong><\/dt>\n<dd>a function of form [latex]f(x)=ax^2+bx+c[\/latex] whose graph forms a parabola in the real plane<\/dd>\n<dt><strong>vertex<\/strong><\/dt>\n<dd>the turning point of the graph of quadratic function<\/dd>\n<\/dl>\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-186\">\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><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>\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":23,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-186","chapter","type-chapter","status-publish","hentry"],"part":160,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/186","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/users\/395986"}],"version-history":[{"count":2,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/186\/revisions"}],"predecessor-version":[{"id":1194,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/186\/revisions\/1194"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/160"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/186\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/media?parent=186"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=186"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/contributor?post=186"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/license?post=186"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}