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Worksheets

Quadratic Transformations

Total questions: 80

Worksheet time: 40mins

Name
Class
Date
1.

Describe the transformation(s):

y = x2 - 3

a)

Translated left 3 units

b)

Translated right 3 units

c)

Translated down 3 units

d)

Translated up 3 units

2.

Describe the transformation(s):

y = x2 + 11

a)

Translated up 11 units

b)

Translated right 11 units

c)

Translated left 11 units

d)

Translated down 11 units

3.

Describe the transformation(s):

y = (x + 4)2

a)

Translated up 4 units

b)

Translated left 4 units

c)

Translated right 4 units

d)

Translated down 4 units

4.

Describe the transformation(s):

y = (x - 2.5)2

a)

Translated left 2.5 units

b)

Translated down 2.5 units

c)

Translated right 2.5 units

d)

Translated up 2.5 units

5.

Describe the transformation(s):

y = -x2

a)

Reflected over the x-axis

b)

Translated down 1 unit

c)

Translated right 1 unit

d)

Vertical compression by a factor of 1

6.

Describe the transformation(s):

y = 2x2

a)

Vertical stretch by a factor of 2

b)

Vertical compression by a factor of 2

c)

Translated up 2 units

d)

Reflected over the x-axis

7.

Describe the transformation(s):

y = 0.25x2

a)

Translated right 0.25 units

b)

Translated up 0.25 units

c)

Vertical stretch by a factor of 0.25

d)

Vertical compression by a factor of 0.25

8.

Describe the transformation(s):

y = -x2 + 3

a)

Reflected over the x-axis

b)

Translated up 3 units

c)

Vertical stretch by a factor of 3

d)

Translated left 3 units

9.

Describe the transformation(s):

y = (x + 6)2 + 3

a)

Translated left 6 units

b)

Translated right 6 units

c)

Translated up 3 units

d)

Translated down 3 units

10.

Describe the transformation(s):

y = 10(x - 11)2

a)

Vertical stretch by a factor of 10

b)

Reflected over the x-axis

c)

Translated left 11 units

d)

Translated right 11 units

11.

Describe the transformation(s):

y = (x - 2)2 - 1

a)

Translated left 1 unit

b)

Translated right 2 units

c)

Translated down 2 units

d)

Translated down 1 unit

12.

Describe the transformation(s):

y = -4x2 + 6

a)

Vertical stretch by a factor of 4

b)

Reflected over the x-axis

c)

Translated up 6 units

d)

Translated right 6 units

13.

Describe the transformation(s):

y = 8x2 + 7

a)

Vertical stretch by a factor of 7

b)

Vertical stretch by a factor of 8

c)

Translated right 8 units

d)

Translated up 7 units

14.

Describe the transformation(s):

y = (x + 18)2 - 11

a)

Translated down 11 units

b)

Translated up 18 units

c)

Translated left 11 units

d)

Translated left 18 units

15.

Describe the transformation(s):

y = -9(x + 8)2 - 4

a)

Vertical stretch by a factor of 9

b)

Translated left 8 units

c)

Translated down 4 units

d)

Reflected over the x-axis

16.

f(x) = x2 + 3 is transformed to become g(x) = x2 + 13. Describe the transformation(s) from f(x) to g(x).

a)

Translated up 13 units

b)

Translated up 10 units

c)

Translated left 3 units

d)

Translated down 13 units

17.

f(x) = (x - 1)2 - 2 is transformed to become g(x) = -(x - 3)2 - 2. Describe the transformation(s) from f(x) to g(x).

a)

Reflected over the x-axis

b)

Translated 2 units left

c)

Translated 2 units right

d)

Translated down 2 units

18.

f(x) = -(x + 10)2 is transformed to become g(x) = (x + 10)2 - 2. Describe the transformation(s) from f(x) to g(x).

a)

Translated down 2 units

b)

Translated left 10 units

c)

Reflected over the x-axis

d)

Translated up 2 units

19.

Bill graphed y = 3x2 + 8 and Joy graphed y = 3x2 + 4. What statement describes the difference between the two graphs?

a)

Joy's graph is wider than Bill's graph.

b)

Joy's graph is half the size of Bill's graph.

c)

Joy's graph is located to the left of Bill's graph.

d)

Joy's graph is located further down on the y-axis than Bill's graph.

20.

Bill graphed y = x2 and Joy graphed y = 3(x + 5)2. What statement(s) describe the difference between the two graphs?

a)

Joy's graph is wider than Bill's graph.

b)

Joy's graph is skinnier than Bill's graph.

c)

Joy's graph is located to the left of Bill's graph.

d)

Joy's graph is located further down on the y-axis than Bill's graph.

21.

Bill graphed y = (x + 7)2 and Joy graphed y = (x - 5)2 + 9. What statement(s) describe the difference between the two graphs?

a)

Joy's graph is located further down on the y-axis than Bill's graph.

b)

Joy's graph is located further up on the y-axis than Bill's graph.

c)

Joy's graph is located to the left of Bill's graph.

d)

Joy's graph is located to the right of Bill's graph.

22.

What would the transformation between the graph of f(x) = x2 + 3 and the graph of g(x) = (x - 2)2 + 3 be?

a)

Translated up 3 units

b)

Translated down 2 units

c)

Translated right 2 units

d)

Reflected over the x-axis

23.

What would the transformation between the graph of f(x) = (x - 7)2 - 2 and the graph of g(x) = (x - 7)2 + 3 be?

a)

Translated up 3 units

b)

Translated right 7 units

c)

Translated down 5 units

d)

Translated up 5 units

24.

What would the transformation between the graph of f(x) = x2 - 11 and the graph of g(x) = -x2 - 11 be?

a)

Reflected over the x-axis

b)

Translated down 11 units

c)

Translated left 11 units

d)

Vertical stretch by a factor of 11

25.

What would the transformation between the graph of f(x) = (x + 5)2 and the graph of g(x) = (x + 9)2 - 1 be?

a)

Translated left 5 units

b)

Translated down 1 unit

c)

Translated left 4 units

d)

Translated right1 unit

26.

Describe the transformation(s) of the parent function in the graph above.

a)

Reflected over the x-axis

b)

Translated up 1 unit

c)

Translated down 1 unit

d)

Translated left 1 unit

27.

Describe the transformation(s) of the parent function in the graph above.

a)

Translated up 2 units

b)

Translated left 2 units

c)

Translated down 2 units

d)

Translated right 2 units

28.

Describe the transformation(s) of the parent function in the graph above.

a)

Translated down 2 units

b)

Translated left 2 units

c)

Reflected over the x-axis

d)

Vertical compression by a factor of 0.5

29.

Describe the transformation(s) of the parent function in the graph above.

a)

Reflected over the x-axis

b)

Vertical stretch by a factor fo 2

c)

Translated left 1 unit

d)

Translated right 1 unit

30.

Describe the transformation(s) of the parent function in the graph above.

a)

Translated left 3 units

b)

Translated up 3 units

c)

Translated right 3 units

d)

Reflected over the x-axis

31.

Describe the transformation(s) of the parent function in the graph above.

a)

Translated up 2 units

b)

Translated right 2 units

c)

Translated left 1 unit

d)

Translated up 3 units

32.

Describe the transformation(s) of the parent function in the graph above.

a)

Vertical stretch by a factor of 2

b)

Translated right 1 unit

c)

Reflected over the x-axis

d)

Translated down 2 units

33.

Describe the transformation(s) of the parent function in the graph above.

a)

Vertical compression by a factor of 0.5

b)

Reflection over the x-axis

c)

Translated 2 units left

d)

Translated 3 units down

34.

Describe the transformation(s) of the parent function in the graph above.

a)

Translated up 3 units

b)

Translated left 3 units

c)

Translated right 3 units

d)

Reflected over the x-axis

35.

How was the red graph transformed to become the blue graph?

a)

Reflected over the x-axis

b)

Translated up 3 units

c)

Translated right 1 unit

d)

Translated left 3 units

36.

How was the red graph transformed to become the blue graph?

a)

Translated right 4 units

b)

Translated left 4 units

c)

Translated down 4 units

d)

Translated up 4 units

37.

How was the red graph transformed to become the blue graph?

a)

Translated up 3 units

b)

Translated right 4 units

c)

Translated down 2 units

d)

Reflected over the x-axis

38.

How was the red graph transformed to become the blue graph?

a)

Translated down 2 units

b)

Translated up 2 units

c)

Translated left 2 units

d)

Reflected over the x-axis

39.

How was the red graph transformed to become the blue graph?

a)

Reflected over the x-axis

b)

Translated down 3 units

c)

Translated right 4 units

d)

Translated up 3 units

40.

How was the red graph transformed to become the blue graph?

a)

Translated down 3 units

b)

Reflected over the x-axis

c)

Translated left 3 units

d)

Vertical stretch by a factor of 2

41.

Which of the following equations best describes the graph above?

a)

y = x2 + 1

b)

y = -x2 + 1

c)

y = -x2

d)

y = -(x + 1)2

42.

Which of the following equations best describes the graph above?

a)

y = x2 + 2

b)

y = x2 - 2

c)

y = (x + 2)2

d)

y = (x - 2)2

43.

Which of the following equations best describes the graph above?

a)

y = 0.25x2 - 2

b)

y = 0.25(x + 2)2

c)

y = 0.25(x - 2)2

d)

y = x2 - 2

44.

Which of the following equations best describes the graph above?

a)

y = (x - 1)2

b)

y = (x + 1)2

c)

y = x2 + 1

d)

y = x2 - 1

45.

Which of the following equations best describes the graph above?

a)

y = (x - 3)2

b)

y = (x + 3)2

c)

y = x2 + 3

d)

y = x2 - 3

46.

Which of the following equations best describes the graph above?

a)

y = (x - 2)2 + 2

b)

y = (x + 2)2 - 1

c)

y = (x - 1)2 - 2

d)

y = (x + 1)2 + 2

47.

Which of the following equations best describes the graph above?

a)

y = x2 - 2

b)

y = 2x2 + 1

c)

y = 2(x - 1)2 - 2

d)

y = 2(x + 1)2 + 2

48.

Which of the following equations best describes the graph above?

a)

y = 0.25x2

b)

y = x2

c)

y = -0.25x2

d)

y = 4x2

49.

Which of the following equations best describes the graph above?

a)

y = (x + 3)2

b)

y = (x - 3)2

c)

y = x2 - 3

d)

y = x2 + 3

50.

Which of the following equations best describes the red graph above?

a)

y = x2 - 3

b)

y = -x2 + 3

c)

y = (x + 3)2

d)

y = -(x - 3)2

51.

Which of the following equations best describes the blue graph above?

a)

y = x2 - 3

b)

y = -(x - 1)2

c)

y = (x - 1)2

d)

y = -(x + 2)2

52.

Which of the following equations best describes the red graph above?

a)

y = (x - 1)2 - 3

b)

y = (x - 1)2 + 3

c)

y = (x + 1)2 + 3

d)

y = (x + 1)2 - 3

53.

Which of the following equations best describes the blue graph above?

a)

y = (x - 5)2 + 3

b)

y = (x + 5)2 - 3

c)

y = (x - 5)2 - 3

d)

y = (x + 5)2 + 3

54.

Which of the following equations best describes the red graph above?

a)

y = (x + 2)2 - 1

b)

y = (x + 2)2 + 1

c)

y = (x - 2)2 + 1

d)

y = (x - 2)2 - 1

55.

Which of the following equations best describes the blue graph above?

a)

y = (x - 2)2 - 3

b)

y = (x + 2)2 - 3

c)

y = (x - 3)2 + 2

d)

y = (x - 3)2 - 2

56.

Which of the following equations best describes the red graph above?

a)

y = -(x + 2)2

b)

y = -(x - 2)2

c)

y = -(x + 2)2 - 1

d)

y = -(x + 1)2 + 2

57.

Which of the following equations best describes the blue graph above?

a)

y = -(x + 3)2 - 2

b)

y = (x - 3)2 + 2

c)

y = (x + 2)2 - 3

d)

y = -(x + 2)2 - 3

58.

Which of the following equations best describes the red graph above?

a)

y = -(x + 4)2

b)

y = (x + 4)2

c)

y = -(x - 4)2

d)

y = (x - 4)2

59.

Which of the following equations best describes the blue graph above?

a)

y = (x - 3)2

b)

y = -(x - 3)2

c)

y = -x2 - 3

d)

y = x2 - 3

60.

Which of the following equations best describes the red graph above?

a)

y = x2 + 3

b)

y = x2 - 3

c)

y = -(x - 3)2

d)

y = -x2 - 3

61.

Which of the following equations describes a quadratic translated up 2 units?

a)

y = x2 + 2

b)

y = x2 - 2

c)

y = (x + 2)2

d)

y = (x - 2)2

62.

Which of the following equations describes a quadratic translated left 1 unit?

a)

y = (x - 1)2

b)

y = (x + 1)2

c)

y = x2 + 1

d)

y = x2 - 1

63.

Which of the following equations describes a quadratic translated left 1 unit and reflected over the x-axis?

a)

y = -x2 - 1

b)

y = x2 - 1

c)

y = (x - 1)2

d)

y = -(x + 1)2

64.

Which of the following equations describes a quadratic translated left 2 units and down 1 unit?

a)

y = (x + 2)2 - 1

b)

y = (x - 2)2 + 1

c)

y = (x + 1)2 - 2

d)

y = (x - 1)2 + 2

65.

Which of the following equations describes a quadratic translated up 10 units and reflected over the x-axis?

a)

y = -x2

b)

y = -10x2

c)

y = -(x + 10)2

d)

y = -x2 + 10

66.

Which of the following equations describes a quadratic translated left 5 units and compressed by a factored of 0.4?

a)

y = 0.4x2

b)

y = (x - 5)2

c)

y = (x + 5)2

d)

y = 0.4(x + 5)2

67.

Which of the following equations describes a quadratic reflected over the x-axis and translated up 7 units?

a)

y = -x2 + 7

b)

y = x2 + 7

c)

y = -x2 - 7

d)

y = -(x - 7)2

68.

Which of the following equations describes a quadratic translated right 1 unit and vertical stretched by a factor of 2?

a)

y = 2x2

b)

y = (x + 2)2

c)

y = 2(x - 1)2

d)

y = 2(x + 1)2

69.

Which of the following equations describes a quadratic translated down 2 units and vertically compressed by a factor of 0.5?

a)

y = 0.5x2 - 2

b)

y = 0.5x2 + 2

c)

y = 2x2 - 0.5

d)

y = 2(x - 0.5)2

70.

Which of the following equations describes a quadratic translated up 4 units and right 2 units?

a)

y = (x + 4)2 + 2

b)

y = (x - 2)2 + 4

c)

y = (x + 2)2 + 4

d)

y = (x - 4)2 - 2

71.

Gerry plotted the equation y = x2 - 3 on a coordinate grid. He wants to translate his graph 4 units left and 3 units up. Which of the following will be the equation of the translated graph?

a)

y = (x + 4)2 + 3

b)

y = (x - 4)2 + 3

c)

y = (x + 4)2

d)

y = (x - 4)2

72.

Gary plotted the equation y = (x - 1)2 + 3 on a coordinate grid. He wants to translate his graph 4 units left and 3 units up. Which of the following will be the equation of the translated graph?

a)

y = (x + 4)2 - 3

b)

y = (x + 4)2 + 3

c)

y = (x - 5)2 + 6

d)

y = (x + 3)2 + 6

73.

Gary plotted the equation y = (x - 1)2 + 3 on a coordinate grid. He wants to reflect his graph over the x-axis and then translated it 2 units down. Which of the following will be the equation of the translated graph?

a)

y = -(x - 1)2 + 1

b)

y = (x - 1)2 + 1

c)

y = -(x - 3)2 + 3

d)

y = -(x - 1)2 + 5

74.

Gary plotted the equation y = (x + 5)2 + 3 on a coordinate grid. He wants to translate his graph 2 units left and 10 units up. Which of the following will be the equation of the translated graph?

a)

y = (x + 7)2 + 7

b)

y = (x + 7)2 + 13

c)

y = (x - 3)2 + 7

d)

y = (x + 3)2 - 13

75.

Gordon plotted the equation y = x2 - 1 on a coordinate grid. He wants to translate his graph 4 units left and 3 units up. Which of the following will be the equation of the translated graph?

a)

y = (x - 4)2 + 3

b)

y = (x + 4)2 + 2

c)

y = (x + 4)2 - 2

d)

y = (x - 4)2 - 3

76.

Gary plotted the equation y = -x2 on a coordinate grid. He wants to translate his graph 4 units right and stretch it by a scale factor of 2. Which of the following will be the equation of the translated graph?

a)

y = 2x2 + 4

b)

y = -2x2 + 4

c)

y = -2(x + 4)2

d)

y = -2(x - 4)2

77.

Gary plotted the equation y = -x2 on a coordinate grid. He wants to translate his graph 4 units down and compress it by a scale factor of 0.5. Which of the following will be the equation of the translated graph?

a)

y = 0.5x2

b)

y = -0.5x2 - 4

c)

y = -0.5x2

d)

y = -x2 - 4

78.

Describe the transformation(s) in the equation below:

y = (x + 10)2 - 124

a)

Translated left 10 units

b)

Translated down 124 units

c)

Translated left 124 units

d)

Translated up 10 units

79.

Describe the following transformation(s) given the equation below:

y = (x - 5)2 - 49

a)

Translated right 5 units

b)

Translated right 49 units

c)

Reflected over the x-axis

d)

Translated down 49 units

80.

Describe the transformation(s) in the equation below:

y = -3(x - 2)2

a)

Reflected over the x-axis

b)

Vertical stretch by a factor of 2

c)

Vertical stretch by a factor of 3

d)

Translated right 2 units