{"id":183,"date":"2023-06-21T13:22:41","date_gmt":"2023-06-21T13:22:41","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/review-topics-for-success-6\/"},"modified":"2023-07-04T03:43:56","modified_gmt":"2023-07-04T03:43:56","slug":"review-topics-for-success-6","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/review-topics-for-success-6\/","title":{"raw":"Review Topics for Success: Quadratic Equations","rendered":"Review Topics for Success: Quadratic Equations"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Outcomes<\/h3>\r\nBy the end of this section, you will be able to:\r\n<ul>\r\n \t<li>Graph quadratic functions using tables and transformations<\/li>\r\n \t<li>Identify important features of\u00a0the graph of a quadratic function of the form [latex]f(x)=ax^2+bx+c[\/latex]<\/li>\r\n<\/ul>\r\n<\/div>\r\nQuadratic functions are especially helpful for modeling real-world situations where a minimum or maximum function value would help solve a problem. They are used to answer questions in\u00a0business, physics, engineering, and more, such as\r\n<ul>\r\n \t<li>What maximum height does a projectile achieve before falling back to the ground and how long after launch will it land?<\/li>\r\n \t<li>What price should be applied to a cup of coffee to maximize revenue?<\/li>\r\n \t<li>What number of units should a factory produce each day to minimize costs?<\/li>\r\n<\/ul>\r\nBefore studying problems such as these, though, it is necessary to define the characteristics of the function and learn what they reveal about the model. You'll need an understanding of the vertex and intercepts (real and complex), different algebraic forms of the quadratic function, and some formulas for quickly identifying certain features.\r\n\r\nIn preparation for studying these functions, take a close look in this review section at the shape of the graph of the function and how it can be used to describe projectile motion in the plane.\r\n\r\nWarm up for this module by refreshing important concepts and skills you'll need for success.\u00a0As you study these review topics, recall that you can also\u00a0return to Algebra Essentials any time you need to refresh the basics.\r\n<div class=\"textbox examples\">\r\n<h3>Recall for success<\/h3>\r\nLook for red boxes like this one throughout the text. They'll show up just in time to give helpful\u00a0reminders of the math you'll need, right where you'll need it.\r\n\r\n<\/div>","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Outcomes<\/h3>\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>Graph quadratic functions using tables and transformations<\/li>\n<li>Identify important features of\u00a0the graph of a quadratic function of the form [latex]f(x)=ax^2+bx+c[\/latex]<\/li>\n<\/ul>\n<\/div>\n<p>Quadratic functions are especially helpful for modeling real-world situations where a minimum or maximum function value would help solve a problem. They are used to answer questions in\u00a0business, physics, engineering, and more, such as<\/p>\n<ul>\n<li>What maximum height does a projectile achieve before falling back to the ground and how long after launch will it land?<\/li>\n<li>What price should be applied to a cup of coffee to maximize revenue?<\/li>\n<li>What number of units should a factory produce each day to minimize costs?<\/li>\n<\/ul>\n<p>Before studying problems such as these, though, it is necessary to define the characteristics of the function and learn what they reveal about the model. You&#8217;ll need an understanding of the vertex and intercepts (real and complex), different algebraic forms of the quadratic function, and some formulas for quickly identifying certain features.<\/p>\n<p>In preparation for studying these functions, take a close look in this review section at the shape of the graph of the function and how it can be used to describe projectile motion in the plane.<\/p>\n<p>Warm up for this module by refreshing important concepts and skills you&#8217;ll need for success.\u00a0As you study these review topics, recall that you can also\u00a0return to Algebra Essentials any time you need to refresh the basics.<\/p>\n<div class=\"textbox examples\">\n<h3>Recall for success<\/h3>\n<p>Look for red boxes like this one throughout the text. They&#8217;ll show up just in time to give helpful\u00a0reminders of the math you&#8217;ll need, right where you&#8217;ll need it.<\/p>\n<\/div>\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-183\">\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":21,"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-183","chapter","type-chapter","status-publish","hentry"],"part":160,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/183","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\/183\/revisions"}],"predecessor-version":[{"id":758,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/183\/revisions\/758"}],"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\/183\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/media?parent=183"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=183"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/contributor?post=183"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/license?post=183"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}