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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.
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