Name
Block _____
Algebra 2 Review
page 1
REVIEW for FINAL
Directions:
 You are not allowed to use a calculator on this review.
1. Simplify
a. log3 ( 271 )
b.
( 94 )
d.
x 2 x 2 y3
x -2
1
c. 8
4
3
e. f(–2) if f(x) = x3 – x2
-2
Algebra 2 Review
2. Suppose f(x) = –2x + 9 and g(x) = 3x 2 +1
Find a function formula for the composition function f(g(x)). Show your work.
3. Solve these equations. Go as far as possible without a calculator.
a. 5x 2 - 2 = 9x
b. log 8 ( x - 8) - 13 = 0
c.
x 2 + 3x -1 = 0
page 2
Algebra 2 Cumulative Test
page 3
4. Sketch the graph of this function:
f(x) = –1 (x + 1)2 (x – 3)
Your graph must have accurately drawn xand y-intercepts and the correct overall
shape.
5. For the graph shown below write a function formula. Show any needed work. Circle your
answers.
6. Convert this quadratic function to vertex form. f(x) = 3x 2 -12x + 23
Algebra 2 Review
page 4
7. A football is kicked into the air. After x seconds, the football’s height in feet is given by
f(x) = –16(x – 2)2 + 64.
a. What is the greatest height reached by the football?
b. Solve the equation f(x) = 48. Explain the meaning of the answer in terms of the football.
c. What are the x-intercepts of the graph of f(x) ? Show or explain how you get your answer.
d. Sketch a graph of f(x) on the given axes.
Label the x-intercept(s), y-intercept, and vertex
with their (x, y) coordinates.
e. What is the domain of f(x)? In other words, what x-values make sense as inputs in this
problem situation?
Algebra 2 Cumulative Test
page 5
8. Let f(x) = – 2x3 + 6x + 4. The table at the right shows some of the function’s
values.
a. Using information from the table, identify one of the factors of f(x).
b. Factor f(x) completely. Show your work.
f(x) = __________________________________________
9. For the graph shown below write a function formula. Show any needed work.
f(x) = __________________________________________
x
1
2
3
f(x)
8
0
–32