{"id":6482,"date":"2013-12-19T15:51:18","date_gmt":"2013-12-19T15:51:18","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=6482"},"modified":"2014-12-02T08:26:55","modified_gmt":"2014-12-02T08:26:55","slug":"solving-quadratic-equations","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/solving-quadratic-equations\/","title":{"rendered":"Solving Quadratic Equations"},"content":{"rendered":"

Overview:<\/strong><\/p>\n

Quadratic equations are very common in algebra.\u00a0 They have the form y = ax2<\/sup> + bx + c, where a is not equal to 0.\u00a0 The graph of a quadratic equation has the shape of a parabola.<\/p>\n

Solving Quadratic Equations By Graphing<\/strong><\/p>\n

Quadratic functions can be graphed on a coordinate plane.\u00a0 They are symmetrical around a single axis of symmetry.\u00a0 Therefore, when solving quadratic functions, one can find approximate values of the roots.\u00a0 For example, suppose the problem is to find two real numbers whose difference is 6 and whose product is 91.\u00a0 If x equals one of the numbers, then x-6 will equal the other number.\u00a0 In addition, x(x-6) = 91.\u00a0 Expanding the equation, \u00a0x2<\/sup> – 6x = 91, or x2<\/sup>-6x -91 =0.\u00a0 The related function, y = x2<\/sup>-6x -91 can be graphed on a coordinate plane.<\/p>\n

Solving Quadratic Equations by Factoring<\/strong><\/p>\n

The above quadratic equation, x2<\/sup>-6x-91, can be solved by factoring.\u00a0 It is a matter of finding what factors will add to -6 and will multiply to 91.\u00a0 That equation can be factored to (x-13)(x+ 7),and if (x-13)(x +7) =0, the ordered pair that will solve the equation is x = 13, 7.\u00a0 There are two ways to see if the equation checks.\u00a0 First, the difference between 13 and 7 is 6, and the product of 13 and 7 is 91.\u00a0 Second, multiplying (13)2<\/sup> is 169-(6\u221913 or 78) =91.<\/p>\n

Solving Quadratic Equations By Completing the Square<\/strong><\/p>\n

Sometimes quadratic equations can be solved by completing the square.\u00a0 For example, an equation such as z2<\/sup>-36 = 28 will also equal z2<\/sup>= 36 + 28 or z2<\/sup> = 64.\u00a0 The square root of 64 is 8.\u00a0 In order for the square to be completed, the quadratic equation on one side must be a perfect square.\u00a0 If the problem is x2<\/sup>+ 6x = 16, it is not a perfect square, but can be made into one, by adding another constant, 9, to each side, so that x2<\/sup>+6x + 9 = 16 +9, or (x +3)2<\/sup>=25, so x +3 =\u221a25.\u00a0 If x +3 = 5 or x +3 = -5, then the two roots of x can equal 2 or -8.<\/p>\n

Solving Quadratic Equations by Using the Quadratic Formula<\/strong><\/p>\n

Any quadratic equation can be solved by using the quadratic formula, as long as the numbers are real, and a is not equal to 0.\u00a0 The quadratic equation x2<\/sup>-6x-91 can also be solved by using the quadratic formula of x=-b \u00b1\u221ab2<\/sup>-4ac all divided by 2.\u00a0 In this example, b = -6, a =1, and c = -91, so underneath the square root sign is 36 + (-4 (-91)) or \u221a36 +364 or \u221a400, which equals 20.\u00a0 -6 \u00b120 all over 2 is either 26\/2 which is 13 or 14\/2, which is 7.<\/p>\n

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Overview: Quadratic equations are very common in algebra.\u00a0 They have the form y = ax2 + bx + c, where a is not equal to 0.\u00a0 The graph of a quadratic equation has the shape of a parabola. Solving Quadratic Equations By Graphing Quadratic functions can be graphed on a coordinate plane.\u00a0 They are symmetrical […]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[339,645,749,1456,1457],"class_list":["post-6482","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-completing-the-square","tag-factoring","tag-graphing","tag-quadratic-equations","tag-quadratic-formula"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6482","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=6482"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6482\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=6482"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=6482"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=6482"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}