Solving quadratic equations is an important skill in algebra.\u00a0 Some methods of solving quadratic equations include factoring, taking the square root of both sides, completing the square, and using the quadratic formula. \u00a0There are many applications where quadratic equations can be used, such as motion, time, distance, and speed.<\/p>\n
A quadratic equation takes the form ax2 <\/sup>+ bx + c = 0, where a, b, and c are all real numbers and the coefficient a is not equal to 0.\u00a0 It is also sometimes called a \u201csecond-degree equation\u201d because the highest exponent is 2.\u00a0 Suppose the equation is 3x2<\/sup> + 15x = -9.\u00a0 It can be changed to the standard form 3x2<\/sup> + 15x + 9 = 0 by adding 9 to both sides.\u00a0 An equation such as 25x2<\/sup> = 16 is also a quadratic equation.\u00a0 There is an a coefficient, no b coefficient, and it can be changed to standard form by subtracting 16 from both sides as 25x2<\/sup> – 16 = 0.<\/p>\n Some quadratic equations can be solved by factoring.\u00a0 Suppose the equation were y2<\/sup>– 36 = 0.\u00a0 If y2<\/sup>is equal to 36, then y will equal the square root of 36 which is 6, or -6.\u00a0\u00a0Sometimes the equation can be solved by expanding the equation first.\u00a0 The equation y2<\/sup>– 36 = 0 can also be expanded to (y – \u221a36)(y + \u221a36) = 0, which has the same solution, y = \u00b16.\u00a0 Similarly, an equation such as (x \u2013 6)2<\/sup> = 64 can be solved by taking the square root of each side so that x – 6 = \u00b18.\u00a0 Solving x \u2013 6 = 8, x = 14.\u00a0 Solving x -6 = -8, x = -2.<\/p>\n If an equation cannot be solved by factoring or taking the square root of both sides, it can be solved by completing the square.\u00a0 In a perfect square trinomial such as x2<\/sup> + 6x + 9, the relationship between the coefficient of x and the 9 is that (1\/2 \u2219 6)2<\/sup> = 9.\u00a0 This principle can be used to solve other quadratic equations.\u00a0 Suppose that the equation were x2<\/sup> + 6x + 8 = 0.\u00a0 This is not a perfect square trinomial (although it is close), but it can be solved by completing the square.\u00a0 First, if x2<\/sup> + 6x = -8, then (1\/2 \u22196)2 <\/sup>would equal the missing term if it were a perfect square trinomial.\u00a0 Substituting that number on both sides \u201ccompletes the square\u201d, so that x2<\/sup> +6x +9 = -8 +9.\u00a0 Then it can be solved the rest of the way, so that x2<\/sup> + 6x + 9 = 1.\u00a0 The complete square is then equal to (x +3)2<\/sup> =1.\u00a0 Taking the square root of each side, x + 3 = 1 or x + 3 = -1 and can be solved as -2 or -4.\u00a0 Substituting the coefficients 1 (for a), 6 (for b) and 8 for c results in the same solution set for x, as (-6 \u00b1 \u221a(36 – 32)\/2 or (-6 \u00b1 2)\/2, which is equivalent to -8\/2(-4) or -4\/2(-2).<\/p>\n Quadratic equations can be used in problems that involve upward motion or motion in more than one direction.\u00a0 For example, suppose a ball is thrown into the air from a hill 3 meters above the ground, at a velocity of 14 meters per second.\u00a0 The constant for gravity on the downward trip is 5x2<\/sup>so that the resulting equation is 5t2<\/sup> – 14t – 3 = 0 which is a quadratic equation.\u00a0 Similarly, problems that involve triangles and use the Pythagorean Theorem can be solved using quadratic equations.<\/p>\n Interested in algebra tutoring services<\/a>? Learn more about how we are assisting thousands of students each academic year.<\/p>\n SchoolTutoring Academy<\/span> is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Kahului, HI: visit Tutoring in Kahului, HI<\/a><\/p>\n","protected":false},"excerpt":{"rendered":" Overview: Solving quadratic equations is an important skill in algebra.\u00a0 Some methods of solving quadratic equations include factoring, taking the square root of both sides, completing the square, and using the quadratic formula. \u00a0There are many applications where quadratic equations can be used, such as motion, time, distance, and speed. What Is a Quadratic Equation? […]<\/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":[2661,339,645,1456,2659,2660],"class_list":["post-6871","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-applications-of-quadratic-equations","tag-completing-the-square","tag-factoring","tag-quadratic-equations","tag-taking-the-square-root","tag-using-the-quadratic-formula"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6871","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\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=6871"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6871\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=6871"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=6871"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=6871"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Can the Equation Be Solved by Factoring?<\/h3>\n
Can the Equation Be Solved by Completing the Square or the Quadratic Formula?<\/h3>\n
What Are Some Applications of Quadratic Equations?<\/h3>\n