Algebra 2
Constructed Response Review
Name _______________________________
Factor. (Sections 5.4 and 6.4)
1. x  17 x  72
2. x  14 x  32
3. x  49
4. 2 x  11x  12
5. x  8
6. 27 x  1
2
2
2
3
For Questions 7-8, solve the system algebraically. (Section 3.2)
7.
2x – 3y = 6
8.
x = -y – 12
9.
2
3
3x + 7y = 15
5x + 2y = -4
Steve is making had-tooled leather belts and wallets to sell at a craft fair. He can bring no more than 20 items to the fair.
Each belt takes 8 hours to make and sells for $45. Each wallet takes 2 hours to make and sells for $15. He has up to 70
hours to spend working on the leather items. He assumes he will sell all the items he makes and wants to make as much
money as possible. (Section 3.4)
a) Write the equations you would use to graph this situation.
b) Write the equation you would use to determine Steve’s profit for this situation. (maximizing his money)
c) Graph this situation and figure out which combination of belts and wallets maximizes his money.
Sections 5.2 and 5.3
10.
f ( x)  x 2  4 x  1
a) Find the line of symmetry.
b) Find the vertex.
8
c) Graph.
6
4
2
-8 -7 -6 -5 -4 -3 -2 -1
1 2 3 4 5 6 7 8
-2
-4
-6
-8
11.
f ( x)  ( x  1) 2  2
a) Find the vertex.
b) Explain the transformation
8
c) Graph.
6
4
2
-8 -7 -6 -5 -4 -3 -2 -1
1 2 3 4 5 6 7 8
-2
-4
-6
-8
12. Write the equation in vertex form.
a)
b)
7
6
5
4
3
2
1
8
7
6
5
4
3
2
1
-3 -2 -1
1
-1
-2
-3
2
3
4
5
6
7
8
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
1 2 3 4 5 6 7
Let f ( x)  2 x and
g ( x)  x 2  4 . Perform each function operation. (Section 7.6)
13. ( f  g )( x)
14. ( f  g )( x)
16. f(-1)
17.
15. f(8)
f ( g (10))
Solve. (Section 7.5)
f ( x)  11x  3  2 x
g ( x)  53 2 x  3  95
19. Find f(x) = 0
20. Find g(x) = 0
(Section 8.5)
21.
Using the given equation
F (n)  440  2
n
12
a) Change the equation from it’s exponential form to
logarithmic form, and solve for n [leave the answer
in terms of F(n)].
F is Frequency and n is number above or below Concert A
b) Which key above (to the right of)
Concert A (n = 0) makes a sound of
frequency 1480 cycles ?
sec
c) What frequency range is played by the
Guitar (key -28 to key +12)?
,
18. g ( f ( x))