Algebra 2
Final Review
Name:_________________________________
Period: ___________
Show all your work for full credit!!!
1) Identify the parent function from the
equation and then graph using
transformations. Describe the
transformation.
𝑔(𝑥) = 𝑥 2 − 1
17) Graph and determine the domain and
2
range: 𝑥−1 − 3 = 𝑓(𝑥)
2) Solve the system.
𝑥 + 3𝑦 + 2𝑧 = 13
2𝑥 + 2𝑦 − 𝑧 = 3
𝑥 − 2𝑦 + 3𝑧 = 6
19) Graph: −4 √𝑥
3) Describe the transformations and graph
based on the transformations.
𝑔(𝑥) = 4(𝑥 − 2)2
4) Graph: 𝑓(𝑥) = 𝑥 2 − 4𝑥 + 3
6
18) Solve: 𝑥 − 𝑥 = 1
3
20) Graph: 𝑥 2 + 𝑦 2 = 81
21) Identify the parent function from the
equation and then graph using
transformations. Describe the
transformation.
𝑔(𝑥) = −√𝑥
𝑥
1
5) Solve: 𝑥 − 7𝑥 − 8 = 0
22) Simplify: 𝑥 2 −4 + 𝑥−2
6) Solve 𝑥 2 = −81
23) Simplify: 𝑥 2 +5𝑥+4
7) Write the quadratic that fits the set of
points: (−1, 8), (0, 6), (1, 2)
24) Write the simplest polynomial with the
roots: −3, 𝑖
8) Find |−3𝑖|
25) Solve: 𝑥+2 =
2
𝑥 2 +𝑥−12
3𝑥
9) Simplify: (8𝑥 3 − 4𝑥 2 − 3𝑥 + 1) −
(1 − 5𝑥 2 + 𝑥)
10) Simplify: 5𝑥 2 (3𝑥 − 2)
11) Divide: (𝑥 3 − 5𝑥 2 + 2𝑥 − 7) ÷ (𝑥 + 2)
12) Graph: 𝑓(𝑥) = 𝑥 3 − 5𝑥 2 + 8𝑥 − 4
13) Write the simplest polynomial with the
roots: −3, 2, 4
14) Simplify:
15) Simplify:
24𝑥 14
𝑥 2 +2𝑥−15
4
𝑥+2
26) Describe the transformation: 𝑔(𝑥) =
−√𝑥 + 1
27) Graph and determine the domain and
3
range: 𝑓(𝑥) = 𝑥+2 + 1
1
28) Graph: 𝑥 = 4 (𝑦 + 1)2
𝑥 2 +4𝑥+3
29) Simplify: 𝑥 2 +2𝑥−8 ÷
3𝑥+3
𝑥−2
30) Graph: 𝑔(𝑥) = 𝑥 3 + 3𝑥 2 + 3𝑥 + 1
9𝑥 16
𝑥−2
2𝑥+2
𝑥 2 −9
÷ 2𝑥−4
𝑥 2 +8
16) Simplify: 𝑥 2 +4 + 𝑥 2 +4
31) Simplify:
2𝑥
𝑥+4
−
3
𝑥+4
32) Divide: (𝑥 3 − 4𝑥 2 + 3𝑥 + 2) ÷ (𝑥 − 3)
Algebra 2
Final Review
Name:_________________________________
Period: ___________
Show all your work for full credit!!!
𝑥+5
9𝑥+3
33) Simplify: 3𝑥+1 ∙ 𝑥 2 −25
34) Write the simplest polynomial with the
roots: √2, √3
35) Graph and determine the domain and
range: 𝑓(𝑥) =
𝑥 2 −3𝑥
𝑥+4
2
2
36) Graph: (𝑥 − 6) + 𝑦 = 361
37) Simplify: 𝑎𝑏 2 (𝑎2 − 𝑎 + 𝑎𝑏)
4𝑥
38) Solve: 𝑥−5 =
53) Simplify: (𝑥 + 4)(𝑥 4 − 3𝑥 2 + 𝑥)
54) Solve: 𝑥 2 − 144
55) Write the quadratic that fits the set of
points: (0,0), (1, −1), (2, −6)
56) Write the equation of the circle with:
𝐶(8, −7), 𝑟 = 14
57) Solve 𝑥 2 − 14𝑥 + 75 − 0
𝑥−5
40) Graph: 𝑓(𝑥) = 𝑥 3 + 𝑥 2 − 2𝑥 − 2
41) Simplify: (5𝑥 − 2𝑥 2 ) + (4𝑥 2 + 6𝑥 −
9)
(𝑥 2 +2𝑥−3) 𝑥−2
∙ 𝑥+3
𝑥 2 −𝑥−2
43) Find |12 − 16𝑖|
1
𝑥 2 −𝑥−𝑥
58) Simplify: (5 − 𝑖) − (11 − 𝑖)
59) Solve: √10𝑥 = 3√𝑥 + 1
60) Write the following in vertex form and
identify the vertex: 𝑓(𝑥) = 𝑥 2 − 4𝑥 + 9
61) Write a function in vertex form.
𝑓(𝑥) = 𝑥 2 is reflected across the 𝑥 - axis
and translated 3 units down to create 𝑔(𝑥)
3
62) Simplify: √27𝑥 6
44) Simplify: (2𝑥 + 5)(𝑥 3 − 𝑥 2 + 1)
45) Simplify:
52) Simplify: (1 + 5𝑖) + (6 − 𝑖)
3𝑥+5
39) Describe the transformation: 𝑓(𝑥) =
√−(𝑥 − 8)
42) Simplify:
51) Graph: 𝑓(𝑥) = 𝑥 2 + 2𝑥 + 3
−
𝑥
63) Write the following in vertex form and
identify the vertex: 𝑓(𝑥) = 𝑥 2 + 2𝑥 − 7
𝑥+2
1
46) Graph and determine the domain and
2𝑥−4
range: 𝑓(𝑥) = 𝑥+3
47) Graph: (𝑥 + 12)2 + (𝑦 − 4)2 = 15
48) Solve 𝑥 2 + 6𝑥 + 10 = 0
49) Solve: √𝑥 + 6 − 7 = −2
𝑥
𝑥
64) Graph: 𝑥 − 4 = − 6 (𝑦 + 2)2
65) Solve 𝑥 2 − 3𝑥 − 8 = 0
66) Solve: √6𝑥 − 12 = 𝑥 − 2
67) Simplify: (5 − 2𝑖)(6 + 8𝑖)
4
3
68) Solve: 𝑥−2𝑥 = 3𝑥−1
2𝑥
50) Solve: 𝑥+4 + 2 = 2𝑥+8
69) Solve: 4𝑥 2 − 16𝑥 + 16 = 0
Algebra 2
Final Review
Name:_________________________________
Period: ___________
Show all your work for full credit!!!
Complete each of the following and show all of your work!
70. Which function has the largest y-intercept?
a.
b. 2𝑥 − 𝑦 = 0
c.
X
-1
3
5
71. Solve the equation for w:
Y
-8
0
4
2𝑙 + 2𝑤 = 𝑝.
72. If Wendy spends $585 to get her computer repaired then write an equation that can be solved to find the time
the repair took.
Time (hours)
Cost ($)
1 hour
105
2 hours
165
3 hours
225
4 hours
285
73. A ball is thrown into the air and the following data is recorded. In what time interval does the ball reach its
maximum height?
X (time in
seconds)
1
2
3
4
Y (height in feet)
47
96
96
13
74. If the vertex of a parabola is given as (5, 97) where x is the time it takes to go y feet high, then what can you
conclude?
75. Given: 𝑓(𝑥) = −𝑥 (𝑥 − 1)3 (𝑥 + 2)2
a. Find the zeros.
b. Determine the multiplicity of the zeros and what that means to the graph (tangent or passes through).
c. Determine the end behaviors.
d. Graph the function.
Algebra 2
Final Review
Name:_________________________________
Period: ___________
Show all your work for full credit!!!
1. Parabola, down 1
2. x = 1, y = 2, z = 3
3. Parabola, squeeze, right 2
26. Flipped and up 1
27. Graph in quad 1 and 3 D: x ≠
-2, R: y ≠1
28. Parabola opens right V(0, -1)
4. Parabola V(2, -1) opens up.
29.
5. x = 8, -1
6. x = 9i
30. (𝑥 + 1)3
2𝑥−3
31.
7. SKIP
32. 𝑥 2 − 𝑥 +
𝑥+3
3(𝑥+4)
𝑥+4
3
51. Parabola opens up V(-1, 2)
52. 7 + 4𝑖
53. 𝑥 5 + 4𝑥 4 − 3𝑥 3 − 11𝑥 2 +
4𝑥
54. 𝑥 = ±12
55. SKIP
56. (𝑥 − 8)2 + (𝑥 + 7)2 = 19
2
𝑥−3
57. 7 ± 𝑖√26
8. SKIP
33.
9. 8𝑥 3 + 𝑥 2 − 4𝑥
10. 15𝑥 3 − 10𝑥 2
11. 𝑥 2 − 7𝑥 + 16 −
34. 𝑥 − 5𝑥 2 + 6
35. SKIP
36. Circle C(6,0) r=19
59. x = 9
60. 𝑓(𝑥) = (𝑥 − 2)2 + 5 V(2, 5)
61. 𝑔(𝑥) = −𝑥 2 − 3
37. 𝑎3 𝑏 2 − 𝑎2 𝑏 2 + 𝑎2 𝑏 3
38. No solution
62. 3𝑥 2
63. 𝑓(𝑥) = (𝑥 + 1)2 − 8 V(-1, 8)
64. Parabola, opens down V(4, 2)
39
𝑥+2
12. cubic (zeros: 1 and 2)
13. 𝑥 3 − 3𝑥 2 − 10𝑥 + 24
14.
15.
8𝑥 2
𝑥−5
4
39. SKIP
3
2(𝑥+5)
𝑥+3
16. x = 1, y = -3
17. Graph in quadrants 1 &3
40. (𝑥 + 1)(𝑥 2 − 2) = 0
Cubic with zeros: -1, ±√2
41. 2𝑥 2 + 11𝑥 − 9
𝑥−1
42.
𝑥+1
58. -6
65.
3±√41
2
66. x = 8, 2
67. x = 2
18. x = 3, -2
19. Graph
20. Circle C(0,0) r =9
43. SKIP
44. 2𝑥 4 + 3𝑥 3 − 5𝑥 2 + 2𝑥 + 5
21. Flip the parent graph to
quadrant 4
2𝑥+2
22.
46. SKIP
71. 𝑤 =
47. Circle C(-12,4) r= √15
72. 𝑦 = 60𝑥 + 45
23.
48. −3 ± 𝑖
73. Between 2 and 3 seconds
24. 𝑥 + 3𝑥 + 𝑥 + 3
49. x = 19
25. x = 2
50. x = 0
74. the ball reaches it’s
maximum height of 97 feet in 5
seconds.
75. a. Zeros: (-2, 0, 1)
b. Crosses at 0 and 1, tangent at
-2
c. 𝑎𝑠 𝑥 → −∞, 𝑓(𝑥) → −∞
𝑎𝑠 𝑥 → ∞, 𝑓(𝑥) → −∞
d. graph degree 6
(𝑥−2)(𝑥+7)
𝑥−3
𝑥+1
3
2
45.
–𝑥 3 +2𝑥 2 +𝑥+1
68. x = 4/9
69. x = 2
70. a
𝑥(𝑥−2)(𝑥+2)
𝑝−2𝑙
2