ALG 2 CH



ALG. 2 CH. 5.5-5.8 TEST PRE-VIEW - QUADRATIC EQUATIONS & FUNCTIONS

CHAPTER REVIEW FOR CH. 5 TEST

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____ 1. The function [pic] models the height y in feet of a stone t seconds after it is dropped from the edge of a vertical cliff. How long will it take the stone to hit the ground? Round to the nearest hundredth of a second.

|a. |7.79 seconds |c. |0.25 seconds |

|b. |11.02 seconds |d. |5.51 seconds |

____ 2. A landscaper is designing a flower garden in the shape of a trapezoid. She wants the length of the shorter base to be 3 yards greater than the height, and the length of the longer base to be 5 yards greater than the height. For what height will the garden have an area of 360 square yards? Round to the nearest tenth of a yard.

|a. |17.1 yards |c. |39.2 yards |

|b. |34.2 yards |d. |152.6 yards |

____ 3. –6 – [pic]

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |[pic] |

____ 4. Identify the graph of the complex number [pic].

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |[pic] |

Solve the equation.

____ 5. [pic]

|a. |14, 4 |c. |14, –14 |

|b. |–4, –14 |d. |–4, 4 |

____ 6. A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter base to be 3 yards greater than the height and the longer base to be 7 yards greater than the height. She wants the area to be 155 square yards. The situation is modeled by the equation [pic]. Use the Quadratic Formula to find the height that will give the desired area. Round to the nearest hundredth of a yard.

|a. |12.7 yards |c. |10.2 yards |

|b. |20.4 yards |d. |320 yards |

Short Answer

7. Determine the type and number of solutions of [pic].

8. Solve by factoring.

[pic] = 0

Solve the equation by finding square roots.

9. [pic]

10. [pic]

11. Simplify [pic] using the imaginary number i.

Write the number in the form a + bi.

12. [pic]

13. Find [pic].

14. Find the additive inverse of [pic].

Simplify the expression.

15. [pic]

16. [pic]

17. [pic]

18. [pic]

Use the Quadratic Formula to solve the equation.

19. [pic]

20. [pic]

21. [pic]

Rewrite the equation in vertex form.

22. [pic]

23. [pic]

24. Use a graphing calculator to solve the equation [pic]. If necessary, round to the nearest hundredth.

Solve the quadratic equation by completing the square.

25. [pic]

26. [pic]

27. [pic]

28. [pic]

Solve the equation.

29. [pic]

30. Find the missing value to complete the square.

[pic]

Essay

31. Use a graphing calculator to graph the function [pic].

|a. |What does the graph let you conclude about real number solutions of [pic]? Explain. |

|b. |Substitute [pic] for x in the equation [pic]. Simplify. Is the resulting equation true? Show your work. |

|c. |What conclusions can you state about solutions of [pic]? Explain. |

ALG 2 CH. 5.4-5-8 Quadratic Equations CHAPTER REVIEW FOR CH. 5 TEST

Answer Section

MULTIPLE CHOICE

1. ANS: D

2. ANS: A

3. ANS: B

4. ANS: B

5. ANS: B

6. ANS: C

SHORT ANSWER

7. ANS:

two real solutions

8. ANS:

–8, [pic]

9. ANS:

[pic], –[pic]

10. ANS:

[pic], [pic]

11. ANS:

[pic]

12. ANS:

[pic]

13. ANS:

[pic]

14. ANS:

[pic]

15. ANS:

[pic]

16. ANS:

[pic]

17. ANS:

–36

18. ANS:

[pic]

19. ANS:

[pic], [pic]

20. ANS:

[pic] [pic]

21. ANS:

[pic] [pic]

22. ANS:

[pic]

23. ANS:

[pic]

24. ANS:

0.87, –2.07

25. ANS:

[pic]

26. ANS:

[pic]

27. ANS:

[pic] [pic]

28. ANS:

[pic] [pic]

29. ANS:

[pic]i, [pic]i

30. ANS:

1

ESSAY

31. ANS:

|[4] |a. |The equation has no real number solutions. The graph of [pic] does not intersect the x-axis. |

| |b. |[pic] |

| | |Yes, [pic] is true. |

| |c. |[pic] has no real number solutions. But the equation does seem to have [pic] as a solution, because you get a |

| | |true equation when you substitute [pic] for x and simplify. |

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