Name _______________________________________ Date ___________________ Class __________________
Algebra 2, L2 Mid-term Review
1. Using f(x)  x2 as a guide, describe the transformation that yields f(x)  7(x  3)2  1.
1
A. compress by a factor of , 3 units left, 1 unit down
7
1
B. stretch by a factor of , 3 units right, 1 unit down
7
C. stretch by a factor of 7, 3 units left, 1 unit down
D. stretch by a factor of 7, 3 units right, 1 unit down
2. If the parent function f(x)  x2 is vertically stretched by a factor of 3, translated 2 units to
the right, then translated 5 units up, write the resulting function g(x) in vertex form.
A. g(x)  3(x  2)2  5
B. g(x)  3(x  2)2  5
3. Consider h(x)  2x2  8x  10. Identify its vertex and y-intercept.
 5 
A.   , 0  ; (2, 18)
 2 
B. (2, 18); (0, 10)
C. (2, 18); (0, 5)
D. (2, 0); (0, 10)
4. Find the minimum or maximum of g(x) x2  2x  8.
A. maximum of (0, 8)
B. minimum of (1, 9)
5. Find all zeros of the trinomial k(x)  x2  2x  24.
A. (6, 0), (4, 0)
B. (4, 0), (6, 0)
C. (0, 4), (0, 6)
D. (1, 25), (0, 24)
6. Solve 81x2  1.
1
A. x  
9
B. x  9
7. Write a quadratic function in standard form having zeros of 5 and 1.
A. h(x)  x2  4x  5
B. h(x)  x2  4x  4
C. h(x)  x2  4x  5
D. h(x)  x2  4x  4
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Holt Algebra 2
Name _______________________________________ Date ___________________ Class __________________
8. Identify the vertex of g(x)  (x  10)2  2.
A. (10, 2)
B. (10, 2)
9. Simplify 9𝑖 2
A. 9
B. -9
10. Solve 36x2  25  0.
A. 6  5i
5
B.  i
6
6
C.  i
5
D. 5  6i
11. Use the Quadratic Formula to solve x2  4x  6  0.
A. 4  2i 2
B. 2  i 2
12. For the discriminant 3x2 + 7x +5 = 0 identify the number of solutions and their type(s).
A. 2 complex solutions
B. 1 real and 1 complex solution
C. 2 real solutions
D. 1 complex solution
13. Selena is standing on a rock cliff that is 52 feet high. She tosses a pebble upward over
the edge, where it hits the top of a 12-foot-high boulder. The quadratic equation that models
the path of the pebble is p(t)  16t 2 12t  52. How long did it take for the pebble to hit the
top of the boulder?
A. 1.25 seconds
B. 1.50 seconds
C. 2.00 seconds
D. 3.25 seconds
14. Simplify (9  2i)(3  i).
A. 12  4i
B. 25  3i
C. 27  i
D. 29  3i
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Holt Algebra 2
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15. Simplify - 8i20
A.8i
B. -8i
C. 8
D. -8
16. Which monomial has the highest degree?
A. 18a5
B. 12a6b
C. 9a4b4
D. 6a2b2c2
17. Which of the following is a fourth degree trinomial with a leading coefficient of 2?
A. x  x2  2x4
B. 2x4  8x3  x  2
18. Which of the following is equal to (3x2  4x  3) minus (x2 2x  3)?
A. 2x2  2x  6
B. 2x2  6x
C. 2x2  6x  6
D. 4x2  2x
19. Which of the following is equal to (x  3)(2x2  4x  1)?
A. 2x3  2x2  11x  3
B. 2x3  2x2  13x  3
20. Which of the following is equal to (x - 7)2?
A. 𝑥 2 − 49
B. 𝑥 2 + 49
C. 𝑥 2 − 14𝑥 − 49
D. 𝑥 2 − 14𝑥 + 49
21. Which of the following is equal to (x3  2x2  3x  6) ÷ (x 2)?
A. x2  3
B. x2  x  3
22. Which of the following is NOT a factor of (x3 x2 14x  24)?
A. x  1
B. x  2
C. x  3
D. x  4
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Holt Algebra 2
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23. Which of the following is the complete factorization of (x4 16)?
A. (x2  4)(x2  4)
B. (x2  4)(x  2)(x  2)
24. If 2i is a root of a polynomial with integer coefficients, which of the following must be
another root?
A. 2
B. -2i
C. i
D. -2
25. Which is a list of all the roots of x3  3x2  28x?
A. {7, 0, 4}
B. {4, 0, 7}
26. Which is a third degree polynomial with 1 and 1 as its only zeros?
A. x3  x2  x  1
B. x3  x2  x  1
C. x3  3x2  3x  1
D. x3  3x2  3x  1
27. Which is a list of all the roots of x3  x2  x  1  0?
A. {1, i, i }
B. {1, i, i }
28. A quintic polynomial has, at most, how many x-intercepts?
A. 3
B. 4
C. 5
D. 6
29. Which is a graph of an even function with a positive leading coefficient?
A
B
C
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Holt Algebra 2
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30. Given f(x)  5x  3 and g(x)  6x  2, find (f  g)(x).
A. 11x  1
B. 11x  5
31. Given f(x)  x  3 and g(x)  4x, find g(f(6)).
A. 3
C. 21
B. 12
D. 24
32. Given f(x)  3x  6 and g(x)  5x, find g(f(x)).
A. 15x  6
B. 15x  30
33. Which is the inverse of f(x)  x  3?
A. y 
1
x 3
B. y  x  3
C. y  x  3
D. y  x  3
34. Given f(x)  2x2  3x  2 and g(x)  7x  4, find (f  g)(x).
A. 2x2  4x  6
C. 2x2  10x  6
2
B. 2x  4x  6
D. 9x2  x  2
35. Given f(x)  3x2  x  1 and g(x)  4x  5, find (gf)(x).
A. 3x2  5x  4
B. 12x3  4x2  4x
C. 12x3  19x2  x  5
D. 12x3  19x2  9x  5
36. Given f(x)  5x  3 and g(x)  x2, find g(f(2)).
A. 7
C. 32
B. 17
D. 49
37. Which function is an example of exponential growth?
A. a(x)  0.5(1.2)x
B. b(x)  2.4(0.86)x
38. Ted’s comic book collection, which was worth $1300 five years ago, has been
increasing in value by 12% per year since then. Which expression gives the current value of
the collection?
A. 1300(1.12)5
C. 1300(1.12)(5)
5
B. 1300(.12)
D. 1300[1  (.12)(5)]
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Holt Algebra 2
Name _______________________________________ Date ___________________ Class __________________
39. The student population of Gloomy Valley High School has been steadily decreasing by
2% per year. If its population 8 years ago was 1200, which is the best expression for its
population now?
A. 1200  1200(.02)8
B. 1200(.98)8
40. Which is the inverse of f  x   2 x  5 ?
A. a  x   x 2 
B. b  x 
5
2
 x  5

2
2
2
C. c  x  
x
5
2
D. d  x  
x2  5
2
41. Which of the following functions is an example of exponential decay?
A. a(x)  0.5(1.2)x
C. c(x)  0.5(x)0.9
B. b(x)  2.4(0.86)x
D. d(x)  log0.5 x
42. Which expression shows the value of a rare postage stamp, originally purchased for
$5000, which has been increasing in value by 11% for 10 years?
A. 5000(0.11)10
B. 5000(1.11)10
C. 5000(11)10
D. 5000(1.11)(10)
43. A balloon with a small leak loses 1% of its volume each day. If it originally contained 24
liters of gas, what is the volume of the gas after one week?
A. 24(.01)7
B. 24(.99)7
C. 24(.01)8
D. 24(.99)8
44. Write 𝑓(𝑥) = 𝑥 2 − 6𝑥 + 11 in vertex form.
A. 𝑓(𝑥) = (𝑥 − 3)2 + 2
C. 𝑓(𝑥) = (𝑥 − 3)2 − 2
B. 𝑓(𝑥) = (𝑥 − 3)2 + 11
D. 𝑓(𝑥) = (𝑥 − 6)2 − 25
45. Which if NOT a factor of 𝑥 4 − 3𝑥 3 − 17𝑥 2 + 39𝑥 − 20?
A. (𝑥 − 1)
C. (𝑥 + 4)
B. (𝑥 + 1)
D. (𝑥 − 5)
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Holt Algebra 2
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46. Which polynomial has the following characteristics: degree = 7; leading coefficient = -5;
number of terms = 3?
A. −5𝑥 7 + 17𝑥 8
B. −5𝑥 2 + 2𝑥 7 + 4
C. 9𝑥 2 − 5𝑥 7 D. 10 − 5𝑥 7 + 8𝑥
47. Which is the equation for the axis of symmetry of the parabola 𝑓(𝑥) = 𝑥 2 − 6𝑥 + 1?
A. 𝑦 = −3
B. 𝑦 = 3
C. 𝑥 = −3
D. 𝑥 = 3
48. If the parent function 𝑓(𝑥) = 𝑥 2 is vertically stretched by a factor of 2, translated 3 units
to the left, then translated 1 unit up, write the resulting function 𝑔(𝑥).
1
C. 𝑔(𝑥) = 2(𝑥 − 3)2 + 1
1
2
D. 𝑔(𝑥) = 2(𝑥 + 3)2 + 1
A. 𝑔(𝑥) = 2 (𝑥 − 3)2 + 1
B. 𝑔(𝑥) = (𝑥 + 3)2 + 1
49. Find the maximum or minimum value of 𝑔(𝑥) = −𝑥 2 + 4𝑥 − 7.
A. Maximum value of -11.
C. Maximum value of -3
B. Minimum value of -11
D. Minimum value of -3
50. Write 𝑓(𝑥) = 𝑥 2 + 6𝑥 − 11 in vertex form.
A. 𝑓(𝑥) = (𝑥 − 3)2 − 20
C. 𝑓(𝑥) = (𝑥 − 6)2 − 11
B. 𝑓(𝑥) = (𝑥 + 3)2 − 20
D. 𝑓(𝑥) = (𝑥 − 6)2 − 11
51. Find the discriminant of the equation: 2𝑥 2 + 3𝑥 − 1 = 0.
A. -1
B. 1
C. 3
D. 17
Free Response:
1. Simplify (𝑥 + 5)2
2. Find all the zeros of 𝑓(𝑥) = 𝑥 2 + 3𝑥 2 + 50.
2. Given 𝑓(𝑥) = 4𝑥 2 + 3𝑥 − 1 and 𝑔(𝑥) = 6𝑥 + 2, find (𝑓 − 𝑔)(𝑥).
3. Find the value of 𝑐 that makes the trinomial a perfect square: 𝑥 2 − 10𝑥 + 𝑐.
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Holt Algebra 2
Name _______________________________________ Date ___________________ Class __________________
1. Given the function 𝑓(𝑥) = −𝑥 2 − 4𝑥 − 7, find the following:
a. The zeros:
b. The axis of symmetry:
c. The maximum or minimum value:
d. The 𝑦-intercept:
e. Graph:
2. Solve for 𝑥 algebraically and graphically: 𝑥 3 − 4𝑥 2 + 4𝑥 = 0
1
3. Given 𝑓(𝑥) = 2 𝑥 + 5, find and graph its inverse.
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Holt Algebra 2