PAP Algebra 2
PAP Algebra 2 Name ____________________________
Fall 2012 Final REVIEW
1. For each parent function (Linear, Quadratic, Absolute Value, Cubic, Inverse Variation, Inverse Squared, Square Root, and Exponential) and their transformations, be able to
a) Sketch the graph (including asymptotes)
b) State the domain and range
c) State which functions are odd, even, or neither
d) State the intervals on which the function is increasing, decreasing, constant, positive, and negative
2. Sketch the graph of a function with domain [-5, 2) and range [1, 4).
3. For the following graph, state the interval(s) for which it is increasing, decreasing, constant, positive, and negative. Then state the domain and range of the function.
4. Given the graph of f(x) below, sketch the graphs of
[pic]
5. Graph the following piecewise function. [pic]
6. Solve the following system by elimination. 7. Solve the following system by graphing:
[pic] [pic]
8. Solve the following system. 9. Graph the following system of linear inequalities:
[pic] [pic]
10. A grocer bought 4 crates of lettuce and 3 crates of cabbage. Later he bought 2 crates of lettuce and 5 crates of cabbage. His first bill was $34.20 and the second bill was $31.80. Find the cost of each crate of lettuce and each crate of cabbage.
11. Santa’s toy factory has devoted Friday, December 14th as the day to make only baby dolls and baseball bats. It takes the elves 5 minutes to make each baby doll and 4 minutes to make each baseball bat. They have at most 12 hours to work on Tuesday and need to make a minimum of 500 toys (dolls and bats). Write a system of linear inequalities to represent this situation.
12. Write the equation of a parabola through (-2, 18), (-6, 54), and (8, -2). Then state it’s domain and range.
13. Find the roots of [pic] using Quadratic Formula.
14. Convert [pic]to standard form.
15. What is the equation of a parabola with the vertex (2, -1) through the point (3, -2)?
16. What is the discriminant of[pic]? What kind and number of solutions will you get?
17. What is the discriminant of[pic]? What kind and number of solutions will you get?
18. Convert [pic]into vertex form.
19. Solve [pic]by completing the square.
20. State the end behavior of each of the following polynomials.
a)[pic] b) [pic] c)[pic]
21. Simplify each of the following:
a) [pic] b) [pic] c) [pic] d) (3 + 4i)(3 – 4i)
22. Find the vertex form and standard form of the quadratic function graphed.
[pic]
23. At the arcade, Sami won 2 blue tickets, 1 yellow ticket, and 3 red tickets for 1500 total points. Jamal won 1 blue ticket, 2 yellow tickets, and 2 red tickets for 1225 points. Yvonne won 2 blue tickets, 3 yellow tickets, and 1 red ticket for 1200 points. Write and solve a system of equations to determine the point value of each type of ticket.
24. Given [pic] [pic] [pic] [pic], find
a) [pic] b) [pic] c) det D d) [pic]
25. Factor and solve each of the following completely.
a) [pic] b) [pic] c) [pic] d) [pic] e)[pic].
26. Factor [pic]
27. Find the missing information about the following polynomial: [pic]
a) Leading Coefficient
b) Degree
c) Number of Real Zeros
d) Number of Unique Zeros
e) Number of Turning Points
f) End Behavior
g) Y-intercept
h) Sketch a graph of the polynomial function
28. A rectangle has an area of [pic]with a width of [pic]. Find the length of the rectangle.
29. A baseball is hit with a velocity of 100 feet per second at an angle of 45 degrees with respect to the ground. The path of the baseball is given by the function [pic], where f(x) is the height of the baseball (in feet) and x is the horizontal distance from home plate (in feet). What is the maximum height reached by the baseball?
30. For [pic], what is the value of k if the y-intercept of the function is (0, -11)?
-----------------------
[pic]
a) [pic] b) [pic]
c) 2f(x) d) [pic]
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