{"id":13432,"date":"2015-12-11T18:03:30","date_gmt":"2015-12-11T18:03:30","guid":{"rendered":"http:\/\/www.oracletutoring.ca\/blog\/?p=13432"},"modified":"2017-09-07T17:01:24","modified_gmt":"2017-09-07T17:01:24","slug":"math-quadratic-functions-finding-the-equation-from-two-points","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/math-quadratic-functions-finding-the-equation-from-two-points\/","title":{"rendered":"Math:  Quadratic functions:  finding the equation from two points"},"content":{"rendered":"<h1>The tutor shows an example of a typical problem involving a quadratic function.<\/h1>\n<p>Consider the following problem:<\/p>\n<p><strong>A quadratic function has vertex (-7,4) and passes through (-4,10). Find its equation.<\/strong><\/p>\n<p>Solution:<\/p>\n<p>Since we are given the vertex, the useful form of the equation to consider is vertex form:<\/p>\n<p>y=a(x-p)^2+q<\/p>\n<p>in which the vertex is (p,q)<\/p>\n<p>For our case, we insert (-7,4) into the equation:<\/p>\n<p>y=a(x-(-7))^2+4<\/p>\n<p>which becomes<\/p>\n<p>y=a(x+7)^2+4<\/p>\n<p>Now, we just need to find the value for a. To do so, we plug in the other given point (-4,10):<\/p>\n<p>10=a(-4+7)^2+4<\/p>\n<p>10=a(3)^2+4<\/p>\n<p>10=9a+4<\/p>\n<p>We subtract 4 from both sides:<\/p>\n<p>6=9a<\/p>\n<p>Next, we divide both sides by 9:<\/p>\n<p>6\/9=a<\/p>\n<p>2\/3=a<\/p>\n<p>Our full equation, and the solution to the problem posed, is<\/p>\n<p>y=(2\/3)(x+7)^2+4<\/p>\n<p>Source:<\/p>\n<p>Travers, Kenneth et al. <u>Using Advanced Algebra<\/u>. Toronto: Doubleday, 1977.<\/p>\n<p>Jack of <a href=\"https:\/\/www.oracletutoring.ca\">Oracle Tutoring by Jack and Diane,<\/a> Campbell River, BC.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The tutor shows an example of a typical problem involving a quadratic function. Consider the following problem: A quadratic function has vertex (-7,4) and passes through (-4,10). Find its equation. Solution: Since we are given the vertex, the useful form &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"more-link\" href=\"https:\/\/www.oracletutoring.ca\/blog\/math-quadratic-functions-finding-the-equation-from-two-points\/\"> <span class=\"screen-reader-text\">Math:  Quadratic functions:  finding the equation from two points<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[1256,1254,655,1255],"class_list":["post-13432","post","type-post","status-publish","format-standard","hentry","category-math","tag-finding-a-quadratic-function-from-two-points","tag-quadratic-function","tag-vertex-form","tag-yax-pq"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/13432","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/comments?post=13432"}],"version-history":[{"count":7,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/13432\/revisions"}],"predecessor-version":[{"id":23431,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/13432\/revisions\/23431"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=13432"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=13432"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=13432"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}