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Holt McDougal Algebra 2

Polynomial Functions Cumulative Test

Select the best answer. 1. If g(x) is a horizontal compression by

a factor of 14

followed by a translation of

3 units down of f(x) = 4x − 5, what is the rule for g(x)? A g(x) = x − 2 C g(x) = 16x − 8 B g(x) = x + 2 D g(x) = 16x + 8

2. Which linear equation best fits this data set?

x 1 4 6 8 11

y 2 3 6 5 8

F 3 55 4

y x= + H y = x + 1

G 2 53 2

y x= + J 4 13 2

y x= −

3. Which of these is the domain and range for the parent function of ( )23 1 2x − + ?

A Domain: 0x ≥ Range: 0y ≥ B Domain: all real numbers Range:

0y ≤ C Domain: all real numbers Range:

0y ≥

D Domain: 0x ≥ Range: 0y ≤

4. Which are the coordinates of the transformed point?

(12, 6); vertical compression of 13

F (1, 0.5) H (4, 2) G (2, 4) J (12, 2)

5. Which completes the table of the transformed function?

Reflection across x-axis A 2, 1, 0, −1, −2 B −2, −1, 0, 1, 2 C 4, 1, 0, −1, − 4 D −5, −4, −3, −2, −1

6. Which of these is the parent function? ( )33 1 9x − +

F 3x H x

G 33x J 1x − 7. Which of these is the parent function?

( )211 2x + −

A x C 2 2x −

B 11x + D 2x 8. Which of these describes the

transformation in terms of f(x)? Vertical shift down 8 units

F ( ) 8f x − H ( )8f x +

G ( )8f x− J ( )8f x −

9. Which transformation describes the equation from its parent equation?

( )22f x

A horizontal shift left 22 units B vertical stretch by a factor of 22 C vertical shift up 22 units D vertical shift down 22 units

10. Which of these describes the transformation in terms of f(x)?

Vertical shift down 13

unit

F ( )13

f x− H ( ) 13

f x −

G ( )13

f x J 13

f x⎛ ⎞+⎜ ⎟⎝ ⎠

11. Which transformation describes the equation from its parent equation?

( )7f x +

A horizontal shift right 7 units B vertical shift up 7 units C horizontal shift left 7 units D vertical stretch by a factor of 7

X y

1 −4

2 −1

3 0

4 1

5 4

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Polynomial Functions Cumulative Test continued

21. What is the simplified version of 18 225i− ?

A −15i C 15i B 15 D −15

22. What is the simplified version of 20 196i − ?

F 14i H 14 G −14i J −14


A −20i C 20 B 20i D −20

24. Use the quadratic formula to solve 23 10 3x x− + .

F 13

x =

H 1, 33

x =

G 3x i= ± J 13, 3

x = − −

25. For the discriminant ( )25 4 4 2,− − ⋅ ⋅ What is the number of solutions and their type(s)? A 2 imaginary solutions B 1 real solution C 1 imaginary solution D 2 real solutions

26. For the discriminant ( )24 4 4 1,− − ⋅ ⋅ What is the number of solutions and their type(s)? F 2 real solutions G 2 imaginary solutions H 1 imaginary solution J 1 real solution

27. Simplify ( )( )10 4 10 4i i− + .

A −210 16i C 10 4− −

B −6 D 26−

28. Simplify 3 41 4

ii

− ++

.

F +13 16

17

i H 13 8i−

G 1317

J 19 817

i− −

29. Simplify ( )( )2 3 2 3i i+ + .

A 7 C 7 6 2i+ B 2 9− + D 9 2i+

30. If the parent function f(x) = x2 is horizontally stretched by a factor of 2, translated 3 units to the left, then translated 1 unit up, write the resulting function g(x) in vertex form.

F ( )21( ) 3 12

g x x= − +

G ( )21( ) 3 12

g x x= + +

H g(x) = 2(x − 3)2 + 1 J g(x) = 2(x + 3)2 + 1

31. Find the minimum or maximum of g(x) = −x2 + 4x −7. A maximum of −11 B minimum of −11 C maximum of −3 D minimum of −3

32. Write a quadratic function in standard form having zeros of −4 and 0.5. F f(x) = x2 − 7x + 4 G g(x) = x2 + 7x + 4 H h(x) = 2x2 − 7x − 4 J j(x) = 2x2 + 7x − 4

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12. Which is the type of correlation shown?

F no correlation H positive G negative J zero


A no correlation C negative B positive D zero

14. Which is the correlation coefficient?

F -0.92 H 0.92 G 0 J 1


A 1 C −0.90 B 0.90 D −1

16. Using 2( )f x x= , what is the transformation

that yields ( )2( ) 3 2 3f x x= + − ?

F vertical stretch of 2, shift 3 units left and 3 units down

G shift 12 units left and 3 units down H vertical stretch of 2, shift 2 units right

and 3 units down J vertical stretch of 3, shift 2 units left

and 3 units down 17. Consider ( ) = + +23 6 2h x x x .What is its

vertex and y-intercept? A vertex: (−1, −1), y-intercept: (0, 2) B vertex: (−2, 2), y-intercept: (0, −2) C vertex: (1, 1), y-intercept: (0, 2) D vertex: (−2, 1), y-intercept: (0, −2)

18. What is the minimum or maximum of ( ) 29 6 1g x x x= − + − ?

F minimum: 1, 03⎛ ⎞⎜ ⎟⎝ ⎠

H minimum: (3, 0)

G maximum: 1, 03⎛ ⎞⎜ ⎟⎝ ⎠

J maximum: (3, 0)

19. What are the zeros of the trinomial 22 3 1x x− + ?

A 12

, 1 C −1, 12

−

B −2, 1 D −1, 2 20. What is a quadratic function in standard

form having zeros of −3 and 12

?

F ( ) 1( ) 32

f x x x⎛ ⎞= + −⎜ ⎟⎝ ⎠

G 2( ) 2 5 3f x x x= + −

H ( ) 1( ) 32

f x x x⎛ ⎞= − +⎜ ⎟⎝ ⎠

J 2( ) 2 5 3f x x x= − −

Chapter

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21. What is the simplified version of 18 225i− ?

A −15i C 15i B 15 D −15


F 14i H 14 G −14i J −14


A −20i C 20 B 20i D −20

24. Use the quadratic formula to solve 23 10 3x x− + .

F 13

x =

H 1, 33

x =

G 3x i= ± J 13, 3

x = − −

25. For the discriminant ( )25 4 4 2,− − ⋅ ⋅ What is the number of solutions and their type(s)? A 2 imaginary solutions B 1 real solution C 1 imaginary solution D 2 real solutions

26. For the discriminant ( )24 4 4 1,− − ⋅ ⋅ What is the number of solutions and their type(s)? F 2 real solutions G 2 imaginary solutions H 1 imaginary solution J 1 real solution

27. Simplify ( )( )10 4 10 4i i− + .

A −210 16i C 10 4− −

B −6 D 26−

28. Simplify 3 41 4

ii

− ++

.

F +13 16

17

i H 13 8i−

G 1317

J 19 817

i− −

29. Simplify ( )( )2 3 2 3i i+ + .

A 7 C 7 6 2i+ B 2 9− + D 9 2i+

30. If the parent function f(x) = x2 is horizontally stretched by a factor of 2, translated 3 units to the left, then translated 1 unit up, write the resulting function g(x) in vertex form.

F ( )21( ) 3 12

g x x= − +

G ( )21( ) 3 12

g x x= + +

H g(x) = 2(x − 3)2 + 1 J g(x) = 2(x + 3)2 + 1

31. Find the minimum or maximum of g(x) = −x2 + 4x −7. A maximum of −11 B minimum of −11 C maximum of −3 D minimum of −3

32. Write a quadratic function in standard form having zeros of −4 and 0.5. F f(x) = x2 − 7x + 4 G g(x) = x2 + 7x + 4 H h(x) = 2x2 − 7x − 4 J j(x) = 2x2 + 7x − 4

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F no correlation H positive G negative J zero


A no correlation C negative B positive D zero


F -0.92 H 0.92 G 0 J 1


A 1 C −0.90 B 0.90 D −1

16. Using 2( )f x x= , what is the transformation

that yields ( )2( ) 3 2 3f x x= + − ?

F vertical stretch of 2, shift 3 units left and 3 units down

G shift 12 units left and 3 units down H vertical stretch of 2, shift 2 units right

and 3 units down J vertical stretch of 3, shift 2 units left

and 3 units down 17. Consider ( ) = + +23 6 2h x x x .What is its

vertex and y-intercept? A vertex: (−1, −1), y-intercept: (0, 2) B vertex: (−2, 2), y-intercept: (0, −2) C vertex: (1, 1), y-intercept: (0, 2) D vertex: (−2, 1), y-intercept: (0, −2)

18. What is the minimum or maximum of ( ) 29 6 1g x x x= − + − ?

F minimum: 1, 03⎛ ⎞⎜ ⎟⎝ ⎠

H minimum: (3, 0)

G maximum: 1, 03⎛ ⎞⎜ ⎟⎝ ⎠

J maximum: (3, 0)

19. What are the zeros of the trinomial 22 3 1x x− + ?

A 12

, 1 C −1, 12

−

B −2, 1 D −1, 2 20. What is a quadratic function in standard

form having zeros of −3 and 12

?

F ( ) 1( ) 32

f x x x⎛ ⎞= + −⎜ ⎟⎝ ⎠

G 2( ) 2 5 3f x x x= + −

H ( ) 1( ) 32

f x x x⎛ ⎞= − +⎜ ⎟⎝ ⎠

J 2( ) 2 5 3f x x x= − −

Chapter

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33. Write c(x) = x2 + 6x − 11 in vertex form. A c(x) = (x − 3)2 − 20 B c(x) = (x + 3)2 − 20 C c(x) = (x − 6)2 − 11 D c(x) = (x − 6)2 − 11

34. Use the Quadratic Formula to solve x2 + x = −1.

F 1 32 2

i− ± H 1 32 2

i±

G 1 52 2

i− ± J 1 52 2

i±

35. Write a quadratic equation that fits the points (2, 27), (4, 61), and (7, 142). A x2 + 10x + 3 C 2x2 + 4x + 13 B x2 + 11x + 1 D 2x2 + 5x + 9

36. Carmen is standing on the ground. She tries to throw a tennis ball over her house, but it hits the roof on the way down at a height of 33 feet. The quadratic equation that models the path of the ball is b(t) = −16t2 + 56t. How long did it take for the ball to hit the roof after it left Carmen’s hand? F 0.75 seconds H 2.25 seconds G 1.5 seconds J 2.75 seconds

37. Simplify 2 41

ii

+−

.

A −2 + 6i C 1 + 5i B −1 + 3i D 2 − 4i

38. Which of the following is a fifth degree trinomial with a quadratic term and a negative leading coefficient? F −1 + 2x5 + 13x2

G −3x5 − 8x3 + 2 H 3x2 − x5 + 12 J x − x2 − 6x4

39. Which of the following is equal to (x2 + x − 2) (3x2 + 4x − 1)? A 3x4 + 7x3 − 3x2 − 9x + 2 B 3x4 + 7x3 − x2 − 9x + 2 C 3x4 + 7x3 − 3x2 − 7x + 2 D 3x4 + 7x3 − x2 − 7x + 2

40. Which of the following is equal to (2p − 3t)4? F 16p4 − 81t

4 G 16p4 − 24p3t + 36p2t

2 − 24pt 3 + 81t

4 H 16p4 − 24p3t + 36p2t

2 − 54pt 3 + 81t

4 J 16p4 − 96p3t + 216p2t

2 − 216pt 3 + 81t

4 41. Which of the following is NOT a factor

of (x4 − 4x3 − 5x2 − 36x − 36)? A x − 2 C x − 3 B x + 2 D x + 3

42. If ( )2 2− and ( )3 2+ are

two of the roots of a fourth degree polynomial with integer coefficients, which of the following is the product of the other two roots?

F 4 2− H 8 5 2−

G 4 2+ J 8 5 2+

43. Which of the following lists all the roots of x3 + 3x = 9 + 3x2?

A {3} C { }3, 3i±

B { }3, 3± D { }3, 3, 3i± ±

44. If f(x) = 2x3 − x2 − x − 4, what is the y-intercept of g(x) = f(x − 2)? F −22 H −14 G −18 J −10

Chapter

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64




15. Something like this:

16. x3 + 4x2 + x − 7 17. g(x) = −x4 − x3 + x2 − 2x + 3 18. y-intercept at −6 and x-intercepts at −1

and 2. 19. 4th 20. Exactly 3 turning points.

Chapter Test Form C 1. Many answers. For example, x5y4z2 2. Many answers. For example,

−4x3 + 3x − 6 3. −x3 + 7x2 − 5x − 3 4. 2x4 − x3 − 6x2 − x + 2 5. p5 + 15p4r + 90p3r2 + 270p2r3 +

405pr4 + 243r5 6. x3 − 2x2 − 6x − 1 7. −2, or 3 8. (−2x + 1)(2x + 1)(4x2 − 2x + 1)

(4x2 + 2x + 1)

9. 5 5− is a double root

10. { 3, 0, 2}− ±

11. x3 + 2x2 − 5x − 10

12. {1, 2 , 2 }i i−

13. 7 14. R(x) → −∞ as x → +∞ and R(x) → −∞ as

x → − ∞

15. Something like this:

16. −x3 − 4x2 + 7 17. g(x) = −x3 − 8x2 − 23x − 21 18. y-intercept unknown; x-intercepts at −0.5

and −3.5. 19. 0 20. Exactly 2 turning points.

Performance Assessment

1. f(x) = 14

(x4 − 9x2 − 4x + 12)

2. {±1, ±2, ±3, ±4, ±6, ±12}

3. f(x) = 14

(x − 1)(x + 2)2(x − 3)

4. x-intercepts: 2 2− , 1, and 3 y-intercept: 3 other points: (−3, 6), (−1, 2), (2, −4),

(4, 27) end behavior: P(x) → +∞ as x → +∞

and P(x) → +∞ as x → −∞



5.

Cumulative Test 1. C 2. F 3. C 4. J 5. C 6. F 7. D 8. F 9. B 10. H 11. C 12. G 13. B 14. F 15. B 16. J 17. A 18. G 19. A 20. G 21. B 22. F 23. D 24. H. 25. A

26. J 27. D 28. F 29. C 30. G 31. C 32. J 33. B 34. F 35. D 36. J 37. B 38. H 39. A 40. J 41. A 42. G 43. C 44. F

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