2. 1.a) Factor: x 2 + 10x + 25 = 0 * Identify a, b and c. a = 1, b = 10, c = 25 (x + 5)(x + 5) = 0 Or (x + 5) 2 = 0 * Place ac and b into the diamond. ac f1f1 b f2f2 25 10 5 5 x 5 * Build factor fractions., x 5 Notice: 5 5 = 25 and 5 + 5 = 10 * Build binomial factors. * Identify the two factors. © 2007- 09 by S-Squared, Inc. All Rights Reserved. Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test

3. b)Use the zero product property to find the solutions. (x + 5)(x + 5) = 0 Factored form Zero Product Property x + 5 = 0 – 5 Subtract x = − 5 1.Factor: x 2 + 10x + 25 = 0 Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test

4. 1.Factor:x 2 + 10x + 25 = 0 c) Check your solutions. x = − 5 x 2 + 10x + 25 = 0 (− 5) 2 + 10(− 5) + 25 = 0 25 – 50 + 25 = 0 − 25 + 25 = 0 0 = 0 Check Equation Simplify Substitute Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test

5. 2.Factor: x 2 – 5x – 24 = 0 * Identify a, b and c. a = 1, b = − 5, c = − 24 * Place ac and b into the diamond. ac f1f1 b f2f2 − 24 − 5 − 8 3 x 3 * Build factor fractions., x − 8 Notice: 3 (− 8) = − 24 and 3 + (− 8) = − 5 * Build binomial factors. (x + 3)(x – 8) = 0 * Identify the two factors. Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test

6. x = 8 2.Factor:x 2 – 5x – 24 = 0 (x + 3)(x – 8) = 0 Factored form Zero Product Property x + 3 = 0 and x – 8 = 0 – 3 Subtract x = − 3 + 8 Add Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test b) Use the zero product property to find the solutions.

7. (x + 9)(x – 9) = 0 3.Factor: x 2 – 81 = 0 * Identify a, b and c. a = 1, b = 0, c = − 81 * Place ac and b into the diamond. ac f1f1 b f2f2 − 81 0 − 9 9 x 9 * Build factor fractions., x − 9 Notice: 9 (− 9) = − 81 and 9 + (− 9) = 0 * Build binomial factors. * Identify the two factors. Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test

8. 3.Factor: x 2 – 81 = 0 (x – 9)(x + 9) = 0 Factored form Zero Product Property x – 9 = 0 and x + 9 = 0 + 9 Add x = 9 – 9 Subtract x = − 9 Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test b) Use the zero product property to find the solutions.

9. Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test a) Factor out the common monomial. 4. Given: 4x 2 – 14x + 6 = 0 2(2x 2 – 7x + 3) = 0 * The greatest common monomial is 2. Factor out a 2.

10. b) Factor the resulting trinomial. * Identify a, b and c. a = 2, c = 3 2(2x – 1)(x – 3) = 0 * Place ac and b into the diamond. ac f1f1 b f2f2 6 − 7− 7 − 6 − 1 2x − 1 * Build factor fractions., 2x − 6 Notice: −1 (− 6) = 6 and − 1 + (− 6) = − 7 * Build binomial factors. * Identify the two factors. Reduce 1 − 3 Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test 4. Given: 4x 2 – 14x + 6 = 0 2(2x 2 – 7x + 3) = 0, b = − 7

11. 2x = 1 c) Use the zero product property to find the solutions. 4. Factor: 4x 2 – 14x + 6 = 0 2(x – 3)(2x – 1) = 0 Factored form Zero Product Propertyx – 3 = 0 and 2x – 1 = 0 + 3 Add x = 3 + 1 Add 1 Divide 2 2 2 x = Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test

12. h = height of the object at time t t = time in seconds s = initial height 5.Using the Vertical Motion Model h = − 16t 2 + s where You are standing on a cliff 784 feet high and drop your cell phone. How long will it take until your phone hits the ground below (h = 0)? h = 0 t = t (need to find) s = 784 * Identify h, t and s. Substitute 0 = − 16t 2 + 784 – 784 Subtract Isolate t 2 − 784 = − 16t 2 Divide −16 49 = t 2 Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test

13. h = height of the object at time t t = time in seconds s = initial height 5.Using the Vertical Motion Model h = − 16t 2 + s where You are standing on a cliff 784 feet high and drop your cell phone. How long will it take until your phone hits the ground below (h = 0)? 49 = t 2 + Square root 7 = t + * Time is always positive. 7 = t It will take 7 seconds for the phone to hit the ground. Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test

14. * Identify a, b and c. a = 1, b = 2, c = − 8 * Place ac and b into the diamond. ac f1f1 b f2f2 − 8 2 − 2 4 x 4 * Build factor fractions., x − 2 Notice: (4)(− 2) = − 8 And 4 + (− 2) = 2 * Build binomial factors. * Identify the two factors. 0 = (x + 4)(x – 2) 6.Complete the following given: a)Let y = 0, factor and solve using the zero product property. y = x 2 + 2x – 8 Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test

15. 6.Complete the following given: a)Let y = 0, factor and solve using the zero product property. a = 1b = 2 c = − 8 Zero Product Property x + 4 = 0 and x – 2 = 0 – 4 Subtract x = − 4 + 2 Add x = 2 0 = (x + 4)(x – 2)Factored form Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test y = x 2 + 2x – 8

16. Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test 6.Complete the following given: b)Identify the x – intercepts. a = 1 b = 2 c = − 8 x = − 4 x = 2 From part (a). * The zeros of the quadratic are also the x – intercepts. (− 4, 0) and (2, 0) * Notice the x – intercepts have a y – coordinate of 0. y = x 2 + 2x – 8

17. − 2 2 y = x 2 + 2x – 8 6.Complete the following given: c) Find the vertex. x = − 4 + 2 2 x = − 1 The x-value of vertex is the mid-point of the x-intercepts. x-value of vertex Simplify * The vertex is the highest or lowest point on a parabola. Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test (− 4, 0) and (2, 0)

18. Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test y = x 2 + 2x – 8 6.Complete the following given: c) Find the vertex. x = − 1 * Substitute into the quadratic equation to find y. y = x 2 + 2x – 8 y = (−1) 2 + 2(− 1) – 8 y = 1 – 2 – 8 y = − 1 – 8 y = − 9 Vertex (−1, − 9) Equation Simplify Substitute

19. 6.Complete the following given: d)Find the y – intercept. y = x 2 + 2x – 8 * Where the graph crosses the y-axis, NOTE: x = 0 (0, − 8) y = x 2 + 2x – 8 y = (0) 2 + 2(0) – 8 y = 0 + 0 – 8 y = − 8 Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test

20. x – intercepts: (− 4, 0) and (2, 0) 6.Complete the following given: e) Graph: Vertex: (− 1, − 9) * Plot the following ordered pairs: y – intercept: (0, − 8) Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test y = x 2 + 2x – 8 You are a Math Super Star