{"id":1347,"date":"2012-09-19T22:45:31","date_gmt":"2012-09-19T22:45:31","guid":{"rendered":"http:\/\/testpreparations.com\/help\/?p=1347"},"modified":"2014-12-02T08:32:01","modified_gmt":"2014-12-02T08:32:01","slug":"sat-math-review-the-vertex-form-of-a-quadratic","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2012\/09\/19\/sat-math-review-the-vertex-form-of-a-quadratic\/","title":{"rendered":"SAT Math Review: The Vertex Form of a Quadratic"},"content":{"rendered":"

The vertex form of a quadratic has the form y = m(x \u2013 s)2<\/sup> + t<\/strong> for some m, s and t. This form is used to easily find the vertex of a quadratic which can be found at point (s, t).<\/p>\n

To take a quadratic in the form y = ax2<\/sup> + bx + c and factor it into y = m(x \u2013 s)2<\/sup> + t, we must complete the square.<\/p>\n

Completing the Square<\/h5>\n

We will use an example to demonstrate. Complete the square of y = 3x2<\/sup> + 12x + 15<\/p>\n

Step 1<\/strong>: Factor out the coefficient of x2<\/sup> from the first two terms.<\/span><\/p>\n

y = 3(x2<\/sup> + 4x) + 15<\/p>\n

Step 2<\/strong>: Calculate 0.25b2<\/sup> where b is the coefficient of x.<\/span><\/p>\n

0.25b2<\/sup> = 0.25(4)2<\/sup> = 4<\/strong><\/p>\n

Step 3: <\/strong>Add and subtract that value inside the brackets to keep the function the same.<\/span><\/p>\n

y = 3(x2<\/sup> + 4x + 4 \u2013 4) + 15<\/p>\n

Step 4<\/strong>: Expand the negative term.<\/span><\/p>\n

y = 3(x2<\/sup> + 4x + 4) + 3<\/p>\n

Step 5: <\/strong>Factor the perfect square.<\/span><\/p>\n

y = 3(x + 2)2<\/sup> + 3<\/p>\n

 <\/p>\n

So our quadratic in vertex form is y = 3(x + 2)2<\/sup> + 3 and the vertex can be found at (-2, 3).<\/p>\n

Additionally we can see that the quadratic opens upwards because the value of both a and m are positive. Thus we can tell there are no real roots because the vertex is above the x-axis and the parabola opens upwards.<\/p>\n

Looking to get ready for the SAT? We can help with SAT<\/a> Prep
\nThis article was written for you by Jeremie<\/strong>, one of the tutors with Test Prep Academy<\/span>.<\/p>\n","protected":false},"excerpt":{"rendered":"

The vertex form of a quadratic has the form y = m(x \u2013 s)2 + t for some m, s and t. This form is used to easily find the vertex of a quadratic which can be found at point (s, t). To take a quadratic in the form y = ax2 + bx + […]<\/p>\n","protected":false},"author":6,"featured_media":1865,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2841,3015,3021,2851],"tags":[3054,645,3253,1940,3342],"class_list":["post-1347","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-act","category-math-act","category-mathematics-sat","category-sat","tag-complete-the-square","tag-factoring","tag-quadratic","tag-vertex","tag-vertex-form"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/1347","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=1347"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/1347\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media\/1865"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=1347"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=1347"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=1347"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}