Pre-Calculus Chapter 2 Review #1 Name ______________________________

1. Find the polynomial with the given zeros.a) b) c)

2. Write the equation of the quadratic in standard form: by completing the square:

Identify the vertex and determine whether it’s a maximum or minimum.

3. Write the equation of the quadratic in standard from that has a vertex: (3, -2) and goes through: (5, 0).What are the x and y intercepts? Sketch the graph.

4. Given the quadratic Identify the vertex, axis of symmetry, x and y intercepts.

5. Wheel Adventure productions estimates that its profit P in hundreds of dollars is , where x is the number of units produced in thousands. How many units must be produced to obtain the maximum profit? What is the maximum profit?

6. a) Identify the x intercepts and their multiplicity b) Sketch the graph.A) B)

7. Use long division to divide the following:

A) B)

8. Using synthetic division, find all the zeros of the polynomial.

A) given that (x + 4) is a factor B) given –7 is a zero.

9. Write as a complex number in simplest form.A) B) C)

D) E) F)

G) H) I)

J) K) L) M)

For #10-11, a) List all the possible zeros of the polynomial b) Use synthetic division to find the actual zeros.

10.

11.

For # 12-13, use the given zero to find all the zeros of the function.

12. , given x = 3i 13. , given x = 5 + 2i

14. Find all holes and/or asymptotes for each (Vertical, horizontal, and/or slant). What is the domain of each?

A. B. C.

15. What are the x and y intercepts of the functions from #14?A. B. C.

16. Solve each equation and list all the zeros by factoring.

A. B.

C.

17. Sketch the graph and fill in the blanks:A.

a) What is the degree?_______b)

c) y- intercept: ( ____,_____ )

18. Find the polynomial with the given zeros: 2, -5, 3 + 2i, 3-2i

19. Find all the possible rational zeros of:

20. Find all the zeros of:

x-intercepts Multiplicity touch or cross

(____,____)    

(____,____)    

(____,____)    

21. Find all the asymptotes:

A. B. C.

Vertical: _______________ Vertical / Hole: __________ Vertical: _______________Horizontal: _____________ Horizontal: _____________ Horizontal: _____________Slant: __________________ Slant: _________________ Slant: __________________

For #22-24, find all the zeros of the equations by factoring.22. 23.

24.

25. Write the equation of the parabola with a vertex of (1,7) and goes through point (2, 5).

26. Write the equation of the parabola in standard form by completing the square:

27. Simplify, write answer in standard form:

A. B. C.