To help you solve Part D<\/strong> of your problem, I need some clarification: You mention factors of the function<\/strong> and y-intercept<\/strong>, but you haven\u2019t provided them. That information is crucial to generating the correct standard form of Jared\u2019s function and writing the explanation.<\/p>\n\n\n\n However, I can give you a generic example<\/strong> showing how to write the standard form of a quadratic equation<\/strong> given its factors (x-intercepts)<\/strong> and y-intercept<\/strong>, which you can adapt to your specific problem.<\/p>\n\n\n\n Suppose Jared\u2019s function has factors (x-intercepts) at x=2x = 2x=2 and x=5x = 5x=5, and the y-intercept is (0,10)(0, 10)(0,10).<\/p>\n\n\n\n The factors (x-intercepts) at x=2x = 2x=2 and x=5x = 5x=5 give the factored form: f(x)=a(x\u22122)(x\u22125)f(x) = a(x – 2)(x – 5)f(x)=a(x\u22122)(x\u22125)<\/p>\n\n\n\n The y-intercept is the point where x=0x = 0x=0, and f(x)=10f(x) = 10f(x)=10. Plug into the equation: 10=a(0\u22122)(0\u22125)10=a(\u22122)(\u22125)10=a(10)a=110 = a(0 – 2)(0 – 5) \\\\ 10 = a(-2)(-5) \\\\ 10 = a(10) \\\\ a = 110=a(0\u22122)(0\u22125)10=a(\u22122)(\u22125)10=a(10)a=1<\/p>\n\n\n\n Now plug in a=1a = 1a=1 and expand the factored form: f(x)=(x\u22122)(x\u22125)=x2\u22125x\u22122x+10=x2\u22127x+10f(x) = (x – 2)(x – 5) \\\\ = x^2 – 5x – 2x + 10 \\\\ = x^2 – 7x + 10f(x)=(x\u22122)(x\u22125)=x2\u22125x\u22122x+10=x2\u22127x+10<\/p>\n\n\n\n So, the standard form<\/strong> is: f(x)=x2\u22127x+10f(x) = x^2 – 7x + 10f(x)=x2\u22127x+10<\/p>\n\n\n\n To write a quadratic function in standard form, we start by understanding the information we\u2019re given: the factors<\/strong> (also known as the x-intercepts or roots) and the y-intercept<\/strong>. The standard form of a quadratic function is: f(x)=ax2+bx+cf(x) = ax^2 + bx + cf(x)=ax2+bx+c<\/p>\n\n\n\n If you are given the roots (let\u2019s say r1r_1r1\u200b and r2r_2r2\u200b), you can first write the function in factored form<\/strong>: f(x)=a(x\u2212r1)(x\u2212r2)f(x) = a(x – r_1)(x – r_2)f(x)=a(x\u2212r1\u200b)(x\u2212r2\u200b)<\/p>\n\n\n\n This form is helpful because the roots directly give you the x-values where the graph crosses the x-axis.<\/p>\n\n\n\n However, to fully determine the equation, you need to know the value of \u201ca\u201d \u2014 the leading coefficient \u2014 which tells you how \u201cwide\u201d or \u201cnarrow\u201d the parabola is, and whether it opens upward or downward. You can find \u201ca\u201d by plugging in a known point on the graph. The most common point used is the y-intercept<\/strong>, which is where x=0x = 0x=0.<\/p>\n\n\n\n By substituting the x and y values of the y-intercept into the factored form, you can solve for \u201ca.\u201d Once \u201ca\u201d is known, substitute it back into the equation. Then, expand the factored form using the distributive property to convert it into standard form. Simplify to get: f(x)=ax2+bx+cf(x) = ax^2 + bx + cf(x)=ax2+bx+c<\/p>\n\n\n\n This is the final answer \u2014 the function written in standard polynomial form.<\/p>\n\n\n\n Use the factors of the function and the y-intercept to find the standard form of the equation representing Jared’s function. Type the correct answer in the box. The Correct Answer and Explanation is: To help you solve Part D of your problem, I need some clarification: You mention factors of the function and y-intercept, but […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-230121","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/230121","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=230121"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/230121\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=230121"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=230121"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=230121"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\nExample Problem<\/strong><\/h3>\n\n\n\n
Step 1: Write the factored form<\/strong><\/h3>\n\n\n\n
Step 2: Use the y-intercept to find \u201ca\u201d<\/strong><\/h3>\n\n\n\n
Step 3: Write the standard form<\/strong><\/h3>\n\n\n\n
\n\n\n\nExplanation<\/strong><\/h3>\n\n\n\n
![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner9-197.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"