COMPASS Practice Test 13 Quadratics

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 = (x - 8)(x + 2) x = {-2, 8}

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

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.

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}

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

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.

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 = 2

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

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

 A. 3  B. 2  C. 5  D. 1  E 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

 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

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

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

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

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