1. Unit 12 Review

2. 1. Simplify a. 𝑖 b. − 𝑖 51

3. 1. Simplify a. 𝑖 b. − 𝑖 51

4. 2. Simplify a. 5−2𝑖 3𝑖 b. 5−2𝑖 2+5𝑖

5. 2. Simplify a. 5−2𝑖 3𝑖 b. 5−2𝑖 2+5𝑖

6. 3. Simplify a. (3-2i)(4+2i) b. (3-2i)-4(4-2i)

7. 3. Simplify a. (3-2i)(4+2i) b. (3-2i)-4(4-2i)

8. 4. Find all the solutions for 𝑥 by the method of your choice. a

9. 4. Find all the solutions for 𝑥 by the method of your choice. a

10. 5. Find all the solutions for 𝑥 by the method of your choice. a

11. 5. Find all the solutions for 𝑥 by the method of your choice. a

12. 6. Find all the solutions for 𝑥 by the method of your choice. a

13. 6. Find all the solutions for 𝑥 by the method of your choice. a

14. 7. Find all the solutions for 𝑥 by the method of your choice. a

15. 7. Find all the solutions for 𝑥 by the method of your choice. a

16. 8. Find all the solutions for 𝑥 by the method of your choice. a

17. 8. Find all the solutions for 𝑥 by the method of your choice. a

18. 9. Find all the solutions for 𝑥 by the method of your choice. a

19. 9. Find all the solutions for 𝑥 by the method of your choice. a

20. 10. An arrow is shot into the air so that its height can be found by the formula ℎ 𝑡 =112−2𝑡−2 𝑡 2 . A) Find the maximum height. B) When does the arrow hit the ground?

21. 10. An arrow is shot into the air so that its height can be found by the formula ℎ 𝑡 =112−2𝑡−2 𝑡 2 . A) Find the maximum height. B) When does the arrow hit the ground?

22. 11. Find the equation of the parabola in vertex form.

23. 11. Find the equation of the parabola in vertex form.

24. 12. Find the following for 𝑗 𝑥 =− 𝑥 2 +6𝑥−8. a
12. Find the following for 𝑗 𝑥 =− 𝑥 2 +6𝑥−8. a. The x-intercepts of 𝑗(𝑥). b. Where 𝑗(𝑥) decreasing? c. The axis of symmetry d. The maximum value

25. 12. Find the following for 𝑗 𝑥 =− 𝑥 2 +6𝑥−8. a
12. Find the following for 𝑗 𝑥 =− 𝑥 2 +6𝑥−8. a. The x-intercepts of 𝑗(𝑥). b. Where 𝑗(𝑥) decreasing? c. The axis of symmetry d. The maximum value

26. 13. Given the equation 𝑓 𝑥 =4 𝑥 , write an equation with the same vertex that is narrower than 𝑓(𝑥).

27. 13. Given the equation 𝑓 𝑥 =4 𝑥 , write an equation with the same vertex that is narrower than 𝑓(𝑥).

28. 14. Given the equation 𝑓 𝑥 =4 𝑥 , write an equation with the same vertex that is wider than 𝑓(𝑥).

29. 14. Given the equation 𝑓 𝑥 =4 𝑥 , write an equation with the same vertex that is wider than 𝑓(𝑥).

30. 15. Given the equation 𝑓 𝑥 =4 𝑥 , write an equation with the same vertex that is a reflection of 𝑓(𝑥).

31. 15. Given the equation 𝑓 𝑥 =4 𝑥 , write an equation with the same vertex that is a reflection of 𝑓(𝑥).

32. 15. Given the equation 𝑓 𝑥 =4 𝑥 , write an equation that is a translation of 𝑓(𝑥) three units left and 5 units up.

33. 15. Given the equation 𝑓 𝑥 =4 𝑥 , write an equation that is a translation of 𝑓(𝑥) three units left and 5 units up.

34. 16. Identify the zeros of the function 𝑔 𝑥 = 𝑥 2 −5𝑥−24.

35. 16. Identify the zeros of the function 𝑔 𝑥 = 𝑥 2 −5𝑥−24.

36. 17. The height of a ball is modeled by the equation ℎ 𝑡 =−256 𝑥− Find the time it takes the ball to reach its maximum height.

37. 17. The height of a ball is modeled by the equation ℎ 𝑡 =−256 𝑥− Find the time it takes the ball to reach its maximum height.

38. 18. The path of a cannon ball is modeled by the graph.
What is the domain and range of the model?

39. 18. The path of a cannon ball is modeled by the graph.
What is the domain and range of the model?

40. 19. The path of a cannon ball is modeled by the graph.
How long did the cannon stay in the air?

41. 19. The path of a cannon ball is modeled by the graph.
How long did the cannon stay in the air?

42. 20. Simplify the following: a) −23 b) −52 c) −64 d) 𝑖⋅𝑖⋅𝑖⋅𝑖⋅𝑖⋅𝑖⋅𝑖

43. 20. Simplify the following: a) −23 b) −52 c) −64 d) 𝑖⋅𝑖⋅𝑖⋅𝑖⋅𝑖⋅𝑖⋅𝑖

44. 21. 𝑓 𝑥 = 𝑥 2 −12𝑥+35 a) Vertex b) x-intercepts c) y-intercept d) max/min value

45. 21. 𝑓 𝑥 = 𝑥 2 −12𝑥+35 a) Vertex b) x-intercepts c) y-intercept d) max/min value

46. 22. 𝑓 𝑥 = 2 3 𝑥+5 2 −7 a) Line of symmetry b) vertex c) domain d) range

47. 22. 𝑓 𝑥 = 2 3 𝑥+5 2 −7 a) Line of symmetry b) vertex c) domain d) range

48. 23. Find the value of 𝑐 that makes the expression a perfect square trinomial: 𝑥 2 −15𝑥+𝑐

49. 23. Find the value of 𝑐 that makes the expression a perfect square trinomial: 𝑥 2 −15𝑥+𝑐

50. 24. Write the quadratic function 𝑦=4 𝑥 2 +16𝑥+7 in vertex form by completing the square. Then identify the vertex.

51. 24. Write the quadratic function 𝑦=4 𝑥 2 +16𝑥+7 in vertex form by completing the square. Then identify the vertex.

52. 25. Which has a greater minimum value?
Statement
True
False
8a. The minimum value of 𝑓(𝑥) is greater than the
minimum value of 𝑔(𝑥).
8b. The value of 𝑥 when 𝑓(𝑥) is at its minimum is less than
the value of 𝑥 when 𝑔(𝑥) is at its minimum.
8c. Both 𝑥 intercepts of 𝑔 𝑥 occur when 𝑥 is greater
than zero.
8d. The line of symmetry of 𝑓(𝑥) is 𝑥=1.

53. 25. Which has a greater minimum value?
Statement
True
False
8a. The minimum value of 𝑓(𝑥) is greater than the
minimum value of 𝑔(𝑥).
8b. The value of 𝑥 when 𝑓(𝑥) is at its minimum is less than
the value of 𝑥 when 𝑔(𝑥) is at its minimum.
8c. Both 𝑥 intercepts of 𝑔 𝑥 occur when 𝑥 is greater
than zero.
8d. The line of symmetry of 𝑓(𝑥) is 𝑥=1.

54. 26. Which has a smaller x-value at the minimum?
Statement
True
False
8a. The minimum value of 𝑓(𝑥) is greater than the
minimum value of 𝑔(𝑥).
8b. The value of 𝑥 when 𝑓(𝑥) is at its minimum is less than
the value of 𝑥 when 𝑔(𝑥) is at its minimum.
8c. Both 𝑥 intercepts of 𝑔 𝑥 occur when 𝑥 is greater
than zero.
8d. The line of symmetry of 𝑓(𝑥) is 𝑥=1.

55. 26. Which has a smaller x-value at the minimum?
Statement
True
False
8a. The minimum value of 𝑓(𝑥) is greater than the
minimum value of 𝑔(𝑥).
8b. The value of 𝑥 when 𝑓(𝑥) is at its minimum is less than
the value of 𝑥 when 𝑔(𝑥) is at its minimum.
8c. Both 𝑥 intercepts of 𝑔 𝑥 occur when 𝑥 is greater
than zero.
8d. The line of symmetry of 𝑓(𝑥) is 𝑥=1.

56. 27. What is the product of the x-intercepts of 𝑔 𝑥 ?
Statement
True
False
8a. The minimum value of 𝑓(𝑥) is greater than the
minimum value of 𝑔(𝑥).
8b. The value of 𝑥 when 𝑓(𝑥) is at its minimum is less than
the value of 𝑥 when 𝑔(𝑥) is at its minimum.
8c. Both 𝑥 intercepts of 𝑔 𝑥 occur when 𝑥 is greater
than zero.
8d. The line of symmetry of 𝑓(𝑥) is 𝑥=1.

57. 27. What is the product of the x-intercepts of 𝑔 𝑥 ?
Statement
True
False
8a. The minimum value of 𝑓(𝑥) is greater than the
minimum value of 𝑔(𝑥).
8b. The value of 𝑥 when 𝑓(𝑥) is at its minimum is less than
the value of 𝑥 when 𝑔(𝑥) is at its minimum.
8c. Both 𝑥 intercepts of 𝑔 𝑥 occur when 𝑥 is greater
than zero.
8d. The line of symmetry of 𝑓(𝑥) is 𝑥=1.