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COMPASS Practice Test 13 Quadratics

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This slide presentation will focus on quadratics. Quadratics will always have a variable raised to the second power, like x 2. Factoring is a skill that will help you find solutions to quadratic equations. 0 = x 2 - 6x - 16 0 = (x - 8)(x + 2) x = {-2, 8}

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Quadratic Formula If you do not like to factor you can always use the quadratic formula. 0 = x 2 - 6x - 16 a = 1 b = -6 c = -16

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1. If x = -1 and y = -2, what is the value of the expression 2x 2 y- 3xy ? A.-24 B.-10 C.-2 D.2 E.10 2x 2 y – 3xy = 2(-1) 2 (-2) – 3(-1)(-2) = 2(1) (-2)- 3(-1)(-2) = -4 – 6 = -10 Answer B We start this practice with a substitution problem, not a quadratic. COMPASS often starts with a substitution problem.

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2. What are the solutions to the quadratic x 2 - 2x - 48 = 0? A. 6 and 8 B. -6 and -8 C. -6 and 8 D. 6 and -8 E. 3 and 16 x 2 - 2x - 48 = 0 (x - 8)(x + 6) = 0 Set each factor to 0 x - 8 = 0 x = 8 x + 6 = 0 x = -6 x = { 8, -6}

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2. What are the solutions to the quadratic x 2 - 2x - 48 = 0? A. 6 and 8 B. -6 and -8 C. -6 and 8 D. 6 and -8 E. 3 and 16 Or you could find the answer with the quadratic formula. a = 1 b = -2 c = 48

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2. What are the solutions to the quadratic x 2 - 2x - 48 = 0? A. 6 and 8 B. -6 and -8 C. -6 and 8 D. 6 and -8 E. 3 and 16 Another way to find the solution is to check each of the answers back into the original equation. This would take a long time, but remember this test is not timed. Try x = 6 Thus we can eliminate answers A and D This process of elimination is a good strategy if you get stuck.

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3. What is the sum of the solutions to the quadratic x 2 - 2x - 48 = 0? A. 14 B. -14 C. 2 D. -2 E. 19 To prevent people from using the process of elimination discussed on the previous slide the questions are sometimes written this way. Find the solution set {-6, 8} Add the solutions -6 + 8 = 2

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4. What is the sum of the solutions of the quadratic equation x 2 + 3x = 28? A. 3 B. -3 C. 11 D. -11 E. 10 First write the equation in standard form. x 2 + 3x - 28 = 0 Using the quadratic formula. a = 1 b = 3 c = -28

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5. What is the sum of the solutions of the quadratic equation 2x 2 - x = 15? A. B. C. D. E. -1 First write the equation in standard form. 2x 2 - x - 15 = 0 Using the quadratic formula. a = 2 b = -1 c = -15

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A. 3 B. 2 C. 5 D. 1 E. -1 6. If the equation x 2 - x = 6 is solved for x, what is the sum of the solutions? First write the equation in standard form. x 2 - x - 6 = 0 Using the quadratic formula. a = 1 b = -1 c = -6

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A. -2, -3 B. 2, 3 C. 1, 6 D. -1, -6 E. -2, 3 7. What are the solutions to the quadratic x 2 - 5x = -6? First write the equation in standard form. x 2 - 5x + 6 = 0 Using the quadratic formula. a = 1 b = -5 c = 6

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8. For all x ≠ 2, A. (x + 5) B. (x - 2) C. (x + 2) D. (x - 3) E. (x + 3) Factor the numerator.

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Now plug x = 5 into each of the answers until you find a match. 8. For all x ≠ 2, A. (x + 5) B. (x - 2) C. (x + 2) D. (x - 3) E. (x + 3) Another way to work this problem is to just make up a number for x. Let x = 5

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A. 16 B. 28 C. -28 D. 60 E. -60 9. If x = -4 is a solution to the equation x 2 + 11x + K = 0, then K = ? First substitute x = -4 into the given equation. Then solve for K. x 2 + 11x + K = 0

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10. What are the solutions to the quadratic x 2 - 10x + 24 = 0? A. 4 and 6 B. -4 and 6 C. -4 and -6 D. 2 and -12 E. -2 and 12 x 2 - 10x + 24 = 0 (x - 4)(x - 6) = 0 x - 4 = 0 x = 4 x - 6 = 0 x = 6 x = { 4, 6}

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