Advanced Algebra 2 - Unit 2 Test Review

Section 1.4: Solving Absolute Value Equations

Solve each equation. Check your solutions.

1. |a − 4| = 3a − 6

2. |b + 5| = 2b + 3

3. 5|q + 6| = 20

4. 3|2a − 4| = 0

5. −6y + 4 = |4y + 12|

6. Victor has a goal of making $75 per week at his after-school job. Last month he was within

$6.50 of his goal. What are the maximum and minimum amounts that Victor might have

made last month?

Section 1.6: Solving Absolute Value Inequalities

Write an absolute value inequality for each graph.

7. 8 8. 8.

Solve each inequality and graph the solution on a number line.

9. |2r + 7| < −1

10. 1

3

|8q + 5| ≥ 7

11. |p − 4| ≤ 11

12. Allie tosses a horseshoe at a stake 25 feet away. The horseshoe lands no more than 2 feet

away from the stake. Write and solve an absolute value inequality that represents the range

of distances the horseshoe travelled.

Section 2.7: Parent Functions and Transformations

Write an equation for the function.

13. 14. What is the equation of the function

graphed?

15. Write the equation of the Absolute Value function with the following transformations:

Vertically compressed by a factor of 1⁄2 ; horizontally reflected and stretched by a factor of

3; Vertex at (-2, 3)

16. Graph the following function: f(x) = −2|x − 4| − 3

Advanced Algebra 2 - Unit 2 Test Review

Please complete it on a separate piece of paper. No calculator except when noted.

Section 4.1: Graphing Quadratic Functions

Determine if there is minimum or maximum value and find the value. Then state domain and range.

17. f(x) = −x

2 – 7x + 1 18. f(x) = x

2 + 12x + 27

Find the y-intercept, equation of axis of symmetry and state the vertex. Make a table of values

which includes the vertex and then graph the function.

19. f(x) = 2x

2– 6x − 9

Graph the following quadratics. List the vertex, AOS, Y intercept, X intercepts, and domain/range.

20. y = −x

2 + 4x + 5 21. y = 2x

2 − 16x + 30

Transformations of Quadratics

Write the function in vertex form, then state the vertex, identify max/min, axis of symmetry, and

determine if it opens up or down.

24. y = 2x

2– 12x + 17

25. y = 3x

2 + 12x – 10

26. y = x

2 + 8x + 16

27. y = x

2 − 4x + 9

28. −2x

2 + 7x = y − 12

Completing the Square

Put the following in vertex form by completing the square. Then identify the vertex.

29. y = 5x

2 + 10x + 7 30. y = 2x

2 − 28x + 99