{"id":1932,"date":"2024-06-24T23:00:31","date_gmt":"2024-06-24T23:00:31","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/?post_type=chapter&#038;p=1932"},"modified":"2025-08-15T02:43:34","modified_gmt":"2025-08-15T02:43:34","slug":"graphs-of-polynomial-functions-apply-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/chapter\/graphs-of-polynomial-functions-apply-it-1\/","title":{"raw":"Graphs of Polynomial Functions: Apply It 1","rendered":"Graphs of Polynomial Functions: Apply It 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n \t<li>Identify key features like zeros, turning points, and end behavior in graphs of polynomial functions<\/li>\r\n \t<li>Find where polynomial functions equal zero using different methods, and understand what these zeros mean<\/li>\r\n \t<li>Create and explain graphs of polynomial functions, connecting how the function is written to what its graph looks like<\/li>\r\n<\/ul>\r\n<\/section>\r\n<p class=\"whitespace-pre-wrap break-words\">A theme park company is designing new roller coasters and uses polynomial functions to model the tracks' heights.<\/p>\r\n\r\n\r\n[caption id=\"attachment_7130\" align=\"aligncenter\" width=\"500\"]<img class=\"wp-image-7130\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/06\/08162631\/pexels-stasknop-1172687-300x200.jpg\" alt=\"\" width=\"500\" height=\"333\" \/> A rollercoaster going upside down; Photo by Stas Knop on Pexels[\/caption]\r\n<p class=\"whitespace-pre-wrap break-words\">Engineers need to analyze various aspects of the tracks including zeros (ground level points), turning points, and end behavior to ensure safety and excitement. They're currently analyzing a segment of track modeled by [latex]f(x) = -0.1(x + 2)\u00b2(x - 1)\u00b3(x - 4)[\/latex], where [latex]x[\/latex] is the horizontal distance in feet from the starting point and [latex]f(x)[\/latex] is the height in feet.<\/p>\r\n\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]31628[\/ohm2_question]<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]31629[\/ohm2_question]<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]31630[\/ohm2_question]<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]31631[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Identify key features like zeros, turning points, and end behavior in graphs of polynomial functions<\/li>\n<li>Find where polynomial functions equal zero using different methods, and understand what these zeros mean<\/li>\n<li>Create and explain graphs of polynomial functions, connecting how the function is written to what its graph looks like<\/li>\n<\/ul>\n<\/section>\n<p class=\"whitespace-pre-wrap break-words\">A theme park company is designing new roller coasters and uses polynomial functions to model the tracks&#8217; heights.<\/p>\n<figure id=\"attachment_7130\" aria-describedby=\"caption-attachment-7130\" style=\"width: 500px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-7130\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/06\/08162631\/pexels-stasknop-1172687-300x200.jpg\" alt=\"\" width=\"500\" height=\"333\" srcset=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/06\/08162631\/pexels-stasknop-1172687-300x200.jpg 300w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/06\/08162631\/pexels-stasknop-1172687-1024x683.jpg 1024w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/06\/08162631\/pexels-stasknop-1172687-768x512.jpg 768w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/06\/08162631\/pexels-stasknop-1172687-1536x1024.jpg 1536w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/06\/08162631\/pexels-stasknop-1172687-2048x1365.jpg 2048w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/06\/08162631\/pexels-stasknop-1172687-65x43.jpg 65w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/06\/08162631\/pexels-stasknop-1172687-225x150.jpg 225w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/06\/08162631\/pexels-stasknop-1172687-350x233.jpg 350w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><figcaption id=\"caption-attachment-7130\" class=\"wp-caption-text\">A rollercoaster going upside down; Photo by Stas Knop on Pexels<\/figcaption><\/figure>\n<p class=\"whitespace-pre-wrap break-words\">Engineers need to analyze various aspects of the tracks including zeros (ground level points), turning points, and end behavior to ensure safety and excitement. They&#8217;re currently analyzing a segment of track modeled by [latex]f(x) = -0.1(x + 2)\u00b2(x - 1)\u00b3(x - 4)[\/latex], where [latex]x[\/latex] is the horizontal distance in feet from the starting point and [latex]f(x)[\/latex] is the height in feet.<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm31628\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=31628&theme=lumen&iframe_resize_id=ohm31628&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm31629\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=31629&theme=lumen&iframe_resize_id=ohm31629&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm31630\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=31630&theme=lumen&iframe_resize_id=ohm31630&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm31631\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=31631&theme=lumen&iframe_resize_id=ohm31631&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":12,"menu_order":19,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":206,"module-header":"apply_it","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1932"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/users\/12"}],"version-history":[{"count":10,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1932\/revisions"}],"predecessor-version":[{"id":7763,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1932\/revisions\/7763"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/parts\/206"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1932\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/media?parent=1932"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=1932"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/contributor?post=1932"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/license?post=1932"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}