Algebra 2
Trimester 2 Final Exam Review
I can graph quadratic equations.
Algebraically find all characteristics, then graph.
1.
y = 2(x + 1)2 + 4
Vertex:
Equation for LoS:
x-intercepts:
2.
y-intercept:
y = (x – 4)(x + 2)
Vertex:
Equation for LoS:
x-intercepts:
3.
y-intercept:
y = x2 + 2x – 3
Vertex:
Equation for LoS:
x-intercepts:
y-intercept:
Name_____________________
4.
y = 3x2 – 4x + 2
Vertex:
Equation for LoS:
x-intercepts:
5.
y 
y-intercept:
1
(x  1)2  2
2
Vertex:
Equation for LoS:
x-intercepts:
6.
y-intercept:
y = -3(x + 1)(x - 1)
Vertex:
Equation for LoS:
x-intercepts:
y-intercept:
I can solve quadratic equations.
Algebraically, solve for the appropriate variable. Show your work!!!
7.
x2 + 4x = y
a.
8.
Find f(0).
b.
Find x when f(x) = 20.
Find y when x = -2.
b.
Find x when y = 15.
b.
Find x when y = 0.
b.
Find x when f(x) = 10
3x2 – 24x = y + 48
a.
11.
Find x when y = 0.
x2 - 6x – 12 = y
a.
10.
b.
f(x) = 4(x – 1)2
a.
9.
Find y when x = 4.
Find y when x = 3
f(x) = -x2 + 4x + 5
a.
Find f(-1)
I can simplify polynomial expressions.
Simplify the expressions.
12.
(3x 4 y 2 )3
13.
(x 2 y 3 )3 x 4
14.
15.
(r 4 s 9 )  (r 2st 0 )
16.
3a 3b 6
6a 3b 2
17.
3x 5
18.
x7
19. 2a b c  3b c
0
2
5
3
7
2x 6 y 5
16x 3 y 2
(4x 2 y 3 )5
4
20.  
x 
2
Perform the indicated operation. Write answers in standard form.
21.
(5x3 – x + 3) + (x3 – 9x2 + 4x)
22.
(x3 + 4x 2 – 5x) – (4x3 + x2 – 7)
23.
(x – 6)(5x2 + x – 8)
24.
(x – 2)2(x + 7)
25.
a.
Write an expression for perimeter as a polynomial in standard form.
3x + 2
b.
Write an expression for area as a polynomial in
6x + 1
standard form.
I can factor polynomials completely.
Factor completely.
26.
x4 - 81
27.
x3 + 5x2 – 9x – 45
28.
3x6 + 12x4 – 96x2
29.
3x2 + 10x – 8
30.
4x5 + 12x2
31.
6x2 – 14x + 8
32.
3x2 - 24
33.
6w4 + 33w2 + 36
34.
14x3 - 40x2 - 6x
I can solve polynomial equations.
Do all solving algebraically.
For questions 35-36, solve parts b and c by factoring.
35.
Given y = 4x4 - 16x3 + 16x2
a. Find y when x is -1
36.
b. Find x when y is 0
c. Find x when y is 64x
b. Find x when f(x) = -6.
c. Find x when f(x) = 0.
Given f(x) = x4 + 7x2
a. Find f(2).
Solve for x.
37.
0 = x3 – 4x2 – 11x + 30
38.
0 = x4 + 15x2 – 16
39.
0 =2x4 - 9x3 + 37x - 30
40.
0 = 2x3 + 3x2 – 8x + 3
Show all work! Write and solve a polynomial equation to find the dimensions of the solid with the given
volume.
41.
V  54 cm3
42.
V = 12 yd3
2x
2x + 3
2x
x -1
x+4
Write a volume equation for the box that can be made when the paper is folded. Find the maximum
volume of the box.
43.
44.
11 in
7 in
10 in
15 in
I can graph polynomial equations.
Identify the characteristics of the graph of each polynomial and sketch the graph. Show all work!!!
45. f(x) = 4(x + 1)(x + 2)(x – 1)
46. h(x) = -½x(x + 4)(x – 3)(x + 1) 47. g(x)= (x + 2)2(x – 1)
End behavior:
End behavior:
End behavior:
x-intercepts:
x-intercepts:
x-intercepts:
Multiplicity of any zero?
Multiplicity of any zero?
Multiplicity of any zero?
y-intercept:
y-intercept:
y-intercept:
48. k(x) = (x + 1)2(x - 1)(x – 3)
49. m(x) = -0.25(x + 5)(x – 2)(x + 1)
50. n(x)=-2(x + 1)2(x – 2)2
End behavior:
End behavior:
End behavior:
x-intercepts:
x-intercepts:
x-intercepts:
Multiplicity of any zero?
Multiplicity of any zero?
Multiplicity of any zero?
y-intercept:
y-intercept:
y-intercept:
Write the equation of the polynomial function shown in the graph.
51.
52.
53.
Solve with your graphing calculator!!
Solve for the appropriate variable.
54.
56.
f(x) = 2(x + 3)2 – 7
55.
g(x) = 3x3 + 4x2 – 6x + 1
a.
f(-1)
a.
find x when g(x) = -7
b.
find x when f(x) = 5
b.
find x when g(x) = 2
c.
find x when f(x) = -10
c.
g(-3.17)
4x4 + 5x2 – 10x + 6 = 15
57.
x + 3 = x2 + 4x – 10
59.
h(x) = -5x2 – 4x + 2
Find the maximum or minimum value of the function.
58.
y = 3x2 + 5x – 7