Free Printable SUBW051525

1.

What is the axis of symmetry?
f(x) = x² - 8x + 15.

a)

x = -4

b)

x = 4

c)

y = 4

d)

y = -4

2.

What is the axis of symmetry of y=2x²-4x+9?

a)

x = 1

b)

x = -1

c)

x = -2

d)

x = 4

3.

Which expression results in 10?

a)

50 - [ 5 + (8 x 5) ]

b)

(10 ÷ 2) + (10 ÷ 2)

c)

(70 ÷ 7) x 10

d)

30 ÷ [ (20 ÷ 4) + 1 ]

4.

(2x + 3)(x - 4)

a)

2x² - 5x - 12

b)

2x² - 8x + 12

c)

2x² - 5x + 12

d)

2x² + 5x - 12

5.

Find the product:
(x - 8)(x + 8)

a)

x² - 64

b)

x² + 64

c)

x² - 8x + 64

d)

x² + 8x - 64

6.

Find the product:

$\left(3x\ +\ 2\right)\left(2x\ +\ 4\right)$

a)

6x² + 16x + 8

b)

5x² + 11x + 6

c)

5x² + 16x + 6

d)

6x² + 11x + 8

7.

Find the product:

$\left(2x-7\right)\left(x+2\right)$

a)

$2x^2-5x+4$

b)

$2x^2+3x+14$

c)

$2x^2-3x-14$

d)

$x^2+3x-14$

8.

Multiply

$2x\left(3x^2+4x\ -6\right)$

a)

$6x^2+8x-12$

b)

$14x^2-12$

c)

$6x^3+8x^2-12$

d)

$6x^3+8x^2-12x$

9.

Multiply (x - 2) (5x² + 3x - 1)

a)

5x³ - 13x² - 7x + 2

b)

5x³ - 10x² + 7x + 2

c)

5x³ - 7x² - 7x + 2

d)

5x³ + 13x² + 7x + 2

10.

Multiply (x² - 5) (x² + 3)

a)

x² - 2x - 15

b)

x⁴ - 2x² - 15

c)

x² - 2x + 15

d)

x⁴ - x - 15

11.

(3b + 5)(2b² + 4b + 1)

a)

6b³ + 22b² + 23b + 5

b)

6b³ + 20b² + 23b + 5

c)

6b³ + 20b² + 19b + 5

d)

6b³ + 22b² + 19b + 5

12.

Factor completely:

$18x^3y+24x^5y^3$

a)

$6\left(3x^3y+4x^5y^3\right)$

b)

$6xy\left(3x^2+4x^4y^2\right)$

c)

$18x^3y\left(6x^2y^2\right)$

d)

$6x^3y\left(3+4x^2y^2\right)$

13.

Factor completely:

$18x^4-27x^3$

a)

$9x^3\left(2x-3\right)$

b)

$3x^3\left(6x-9\right)$

c)

$9x^2\left(2x^2-3x\right)$

d)

$3x^2\left(6x^2-9x\right)$

14.

Factor
2a² + 5a + 3

a)

(2a+3)(a+1)

b)

Not factorable

c)

(2a+1)(a+3)

d)

(2a-1)(a-3)

15.

Factor: 3n² + 14n + 8

a)

(3n + 2)(n + 4)

b)

(3n + 4)(n + 2)

c)

(3n + 8)(n + 1)

d)

(3n + 1)(n + 8)

16.

Factor: 4x² - 20x + 25

a)

(4x - 25) (x - 1)

b)

(2x + 5) (2x - 5)

c)

(2x - 5)²

d)

(4x - 5) (x - 5)

17.

Factor:
3x²-12x-15

a)

(3x-15)(x+1)

b)

(3x+5)(x-3)

c)

(x-5)(3x+3)

d)

(x+3)(3x-5)

18.

Factor

5x² - 28x + 32

a)

(3x - 10)(x + 6)

b)

(x - 8)(5x - 4)

c)

(5x - 8)(x - 4)

d)

(5x - 8)(x + 7)

19.

Factor:
x² - 64

a)

(x + 8)(x + 8)

b)

Prime

c)

(x - 8)(x + 8)

d)

(x - 8)(x - 8)

20.

Which transformation transforms the graph of
f(x) = x² to the graph of g(x) = (x + 4)²?

a)

a vertical translation 4 units up

b)

a vertical translation 4 units down

c)

a horizontal translation 4 units to the left

d)

a horizontal translation 4 units to the right

21.

How did we transform from y = x² to y = 2x²?

a)

vertical stretch

b)

horizontal compression

c)

reflection in y-axis

d)

vertical shift up

22.

If the blue graph is
f(x) = x²
the red must be...

a)

g(x) = (x + 3)²

b)

g(x) = (x - 3)²

c)

g(x) = x² + 3

d)

g(x) = x² - 2

23.

If the blue graph is
f(x) = x²
the red must be...

a)

g(x) = (x + 3)²

b)

g(x) = (x - 3)²

c)

g(x) = x² + 3

d)

g(x) = x² - 2

24.

In the equation g(x)=3/4(x-5)²+2, what happens to the parabola?

a)

Vertical compress by 3/4, right 5, up 2

b)

Reflect, horizontal stretch by 3/4, right 5, up 2

c)

Horizontal stretch by 3/4, left 5, up 2

d)

Vertical stretch by 3/4, right 5, up 2

25.

In the equation f(x)=5(x+3)²-10, what does the 5 do?

a)

Vertical stretch by 5

b)

Horizontal compress by 5

c)

Reflect

d)

Move up 5

26.

Does the graph of this equation widen or narrow from the parent function?
y = 5(x - 5)² + 3

a)

widen

b)

narrow

c)

neither

27.

If the blue graph is
f(x) = x²
then the red must be...

a)

g(x) = x²- 5

b)

g(x) = x²+ 5

c)

g(x) = (x - 5)²

d)

g(x) = (x + 5)²

28.

What are the transformations from $g\left(x\right)=x^2$ to $k\left(x\right)=2\left(x-4\right)^2$ ?

a)

Vertical stretch by 2, right 4

b)

Vertical compress by 2, left 4

c)

Vertical stretch by 2, left 4

d)

Vertical compress by 2, right 4

29.

What are the transformations of the following polynomial from the parent function $f\left(x\right)=x^3$ ?

$g\left(x\right)=-2x^3+4$

a)

Vertical compression by a factor of 2, and shifted left by 4 units

b)

Reflected over the x-axis, vertical stretch by a factor of 2, and shifted up 4 units.

c)

Reflected over the y-axis by a factor of 2, and shifted up by 4 units.

d)

None

30.

Which could be the resulting function?

a)

$g\left(x\right)=1.5\left(x-3\right)^3+4$

b)

$g\left(x\right)=0.5\left(x+2\right)^3+8$

c)

g(x)= 2 (x - 3) + 4

d)

$g\left(x\right)=2\left(x+3\right)^3+4$

31.

Which equation describes the transformation of shifting f(x)=x³ three units left?

a)

x³ + 3

b)

x³ - 3

c)

(x + 3)³

d)

(x - 3)³

32.

What are the transformations of this function compared to the parent function y = √(x)?

a)

Shifted right 5, shifted down 2, and reflected over the x-axis

b)

Reflected over the x-axis, vertical stretch, and shifted right 5

c)

Reflected over the x-axis, vertical stretch, and shifted left 5

d)

Shifted right 5, shifted down 2

33.

g(x) = -f(x)
Describe the transformation to f(x) that results in g(x).

a)

f(x) has been reflected over the x-axis.

b)

f(x) has been reflected over the y-axis.

34.

When you add a constant to y=x² what happens to the graph? (Eg y = x² + 2)

a)

Graph moves UP

b)

Graph moves to the RIGHT

c)

Graph moves DOWN

d)

Graph moves to the LEFT

35.

Describe the transformations that map
y = g(x) to y = -g(x + 6) - 10

a)

Reflect over y-axis
Shifted down 10 units
Shifted left 6 units

b)

Reflect over x-axis
Shifted up 10 units
Shifted left 6 units

c)

Reflect over y-axis
Shifted up 10 units
Shifted right 6 units

d)

Reflect over x-axis
Shifted down 10 units
Shifted left 6 units

36.

What are the following transformations:
f(-x) - 4

a)

reflection over the x axis and 4 units right

b)

reflection over the x axis and 4 units down

c)

reflection over the y axis and 4 units right

d)

reflection over the y axis and 4 units down

37.

What are the following transformations?
- f(x+2)

a)

reflection over the y axis and 2 units to the right

b)

reflection over the x axis and 2 units right

c)

reflection over the y axis and 2 units left

d)

reflection over the x axis and 2 units left

38.

Which equation represents a horizontal stretch by a factor of 4 and a vertical translation down 9?

a)

$g(x)=\frac{1}{4}x^3+9$

b)

$g(x)=\frac{1}{4}x^3-9$

c)

$g(x)=4x^3+9$

d)

$g\left(x\right)=4x^3-9$

39.

Describe the transformation:

f\left(x+2\right)

a)

Up 2

b)

Down 2

c)

Right 2

d)

Left 2

40.

Describe the transformation:

$\frac{1}{2}f\left(x\right)$

a)

Vertical Shrink by 1/2

b)

Vertical Stretch by 2

c)

Up 1/2

d)

Right 1/2

41.

Subtract the following polynomials:
(4x³ + 5x² - 2) - (x³ - 3x² + 4)

a)

3x³ + 8x² - 6

b)

3x³ + 2x² + 2

c)

5x³ + 2x² - 6

d)

3x³ + 8x² + 2

42.

Add the following polynomials:
(x³-6x²+3)+(3x³+4x-1)

a)

4x³-2x²+2

b)

4x³-6x²+4x+2

c)

-2x³+2x+2

d)

4x³-2x²-2

43.

What is the relative max?

a)

y = 36 at x = 0

b)

y = -6.55 at x = -2.55

c)

(-∞, ∞)

d)

None

44.

What is the relative max of this function?

a)

x = 5

b)

infinity

c)

there is no relative maximum

d)

2.5 and it occurs at x = 5

45.

The blue dot on this graph represents a(n)...

a)

Absolute Maximum

b)

Absolute Minimum

c)

Relative Maximum

d)

Relative Minimum

46.

What is the x-intercept for the given graph?

a)

1

b)

-2

c)

2

d)

1/2

47.

_{What is the y-intercept of the line?}

a)

y = 1/2

b)

y = 1

c)

y = -1/2

d)

y = -1

48.

What is the y-intercept?

a)

7

b)

0

c)

1

d)

2

49.

Over what interval does the function increase?

a)

[-2, 1]

b)

[1, 4]

c)

[-6, 3]

d)

(-∞, 1]

50.

Over what interval does the function increase?

a)

(−2.5, 2.5)

b)

(0, 5)

c)

(0, 55)

d)

(−5, 0)

51.

Where is the function increasing?

a)

(4, ∞)

b)

(−4, ∞)

c)

(6, ∞)

d)

4 < x < 6

52.

What are the local maxima of this graph?

a)

3.9 at x = 2.2

b)

-3.3 at x = -2.5

c)

-8 at x = 5 and 2.2 at x = 3.9

d)

5 at x = -8 and 3.9 at x = 2.2

53.

Over what interval is this function constant?

a)

(−5, ∞)

b)

(−3, 4)

c)

(4,∞)

d)

(−5)

54.

What is the interval of increase for this function?
There are no arrows on the graph.

a)

(-6, -2)

b)

(-∞,+∞)

c)

[-6, -2]

d)

(-1, 3)

55.

Write a polynomial function that has the given zeros.
x = 2, 4

a)

(x -4) (x-2)

b)

(x-2) (x+4)

c)

(x-2) (x+4)

56.

Name the roots for the equation
y = (x - 12)(x - 2) .

a)

(0, 12) and (0, 2)

b)

(-12, 0) and (-2, 0)

c)

(12, 0) and (2, 0)

d)

(0, -12) and (0, -2)

57.

Write a quadratic equation given the x intercepts and one other point.

Step 1: Write the factors.

The intercepts of this function are (6, 0) and (8, 0). Write the factors.

a)

(x-6) and (x-8)

b)

(x+6) and (x+8)

c)

(x-6) and (x+8)

d)

(x+6) and (x-8)

58.

On which interval(s) is the given function increasing?

a)

(-∞, 2) U (-2, ∞)

b)

(-2, 2) U (-2, ∞)

c)

(-∞, -2) U (0.5, ∞)

d)

(0, 2) U (0.5, ∞)

59.

Describe the intervals over which the given function is decreasing.

a)

(-∞, 0) U (2, ∞)

b)

(5, -4) U (2, -3)

c)

(-3, 0) U (2, 3)

d)

(5, -4) U (0, -3)

60.

How would you describe the behavior of this function on the domain interval (-1, 1)?

a)

increasing

b)

decreasing

c)

constant

61.

Which coordinate would qualify as the *absolute maximum* of this function?

a)

∞

b)

(0, 4)

c)

3

d)

(4, 0)

62.

Describe the interval over which the given function is decreasing.

a)

(-∞, 4)

b)

(4, 3)

c)

(0, 1)

d)

(0, -∞)

63.

Which coordinate point describes the location of the absolute minimum point of this function?

a)

(-2, -1)

b)

(0, -1)

c)

(-1, -2)

d)

(-5, 3)

64.

Find the average rate of change of f(x)=2x²+3x-1 from 1 to 2.

a)

18

b)

-9

c)

9

d)

3

65.

What is the formula for ARC?

a)

y₂-y₁ / x₂-x₁

b)

x₂-x₁ / y₂-y₁

66.

Average Rate of Change is also known as...

a)

y-intercept

b)

x-intercept

c)

linear

d)

slope

67.

At 0 seconds, Mrs. Taylor was 10 feet off the ground. At 5 seconds, she was 20 feet off the ground. What is her rate in feet per second?

a)

10 feet per second

b)

5 feet per second

c)

2 feet per second

d)

6 feet per second

68.

What is the average rate of change of y = 2(3)^x at [2, 4]?

a)

72

b)

3

c)

36.8

d)

630

SUBW051525

Total questions: 68

Worksheet time: 3hrs 19mins

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