Algebra 2 Chapter 5 Review Sophomore

Algebra 2 Chapter 5 Review Sophomore

Davis

Section 1: Graphing Quadratic Functions and Quadratic Inequalities Graph each of the quadratic functions. Write each equation in vertex form, state the vertex, axis of symmetry, and x-intercepts of each graph. (3 pts for each function) 1 1. y ( x 1)( x 5) 3

Vertex Form:

_____________________

Vertex:

______________

Axis of Symmetry:

______________

x-intercepts:

______________

2. y

2 x2 8x 5

Vertex Form:

_____________________

Vertex:

______________

Axis of Symmetry:

______________

x-intercepts:

______________

3. y

( x 3)2 1

Vertex Form:

_____________________

Vertex:

______________

Axis of Symmetry:

______________

x-intercepts:

_____________

Section 2: Zero Product Property Solve the quadratic equation by factoring. (3 points each) 4. 3x3 108x 0

5. 9 x 2 6 x

1

6. 4 x2 15 28x

Section 3: Simplifying Expressions Simplify the expression. Write any complex numbers in standard form. (2 points each) 7.

72

10. 7i

8.

8 4 162

11. (7 9i) (11 13i)

9.

98 3

12.

9 3 i

9 8

Algebra 2 Chapter 5 Review Sophomore

Davis

Section 4: Finding Zeros Determine the value(s) of the zero(s) of each function. (3 points each) 13. y

x2 8x 3

14. y 13x

x2

42

Section 5: The Discriminant Determine the value of the discriminant of the equation and state the number and type of solutions of the equation. (3 points each) 15. 7 x 2 x 10 0

Discriminant = _______________ Number and Type of Solutions: __________________ 16. x 2 8x 5 0

Discriminant = _______________ Number and Type of Solutions: __________________ 17. 2 x2 18x 13 0

Discriminant = _______________ Number and Type of Solutions: __________________

Section 6: Solving Quadratic Equations Solve the quadratic equation using any method. Show all work!! (3 points each) 18. 5x2 60 x 180 0

19. 5 x 2 6 x 7

20. 3( x 9) 2

21. 5 x 2

22

x2 4 x

81

13

Section 7: Powers of i Evaluate the expression. The only degree of i allowed in any expression is 1. (2 pts) 22. 5i 23 14i 2 4i 37

23. i 23,479

24. 15i 2 4i 4

Section 8: Grab Bag Answer each question completely. Be sure to show all work. There will also be one word problem and one mystery problem. Study the following extra problems from the book: p.254 #51, 52, 53; p.262 #101; p.268 #71, 73; p.288 #90, 91 p.316 #33-35