Free Printable Unit 2 Quadratics Writing & Transformations

Worksheets

Unit 2 Quadratics Writing & Transformations

Total questions: 114

Worksheet time: 8hrs 51mins

Name

Class

Date

Does the graph of this equation widen or narrow from the parent function?

y = 3/4x²

widen

neither

narrow

What is the vertex of this equation?
y = -(x - 5) + 4

(5, 4)

(4, 5)

(-5, 4)

(4, -5)

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

widen

narrow

neither

What is the equation in vertex form?

y = -4(x + 3)² - 4

y = -4(x - 3) - 4

y = -4(x + 3)² + 4

y = -4(x - 3)² - 4

Write the equation of the quadratic function that has a x-intercepts at 2 and 4 and passes through the point (3, 4).

y = -4(x - 2)(x - 4)

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

y = 4(x - 2)(x - 4)

y = -0.25(x - 2)(x - 4)

Match the description to its equation.
- moves down 3

Match the description to its equation.
Moves right 7

If the blue is f(x)=x^2,the red must be

g(x)=(x+3)²

g(x)=(x-3)²

g(x)=x²+3

g(x)=x²-2

If the blue is f(x)=x^2,then the red must be

g(x)=x²-5

g(x)=x²+5

g(x)=(x-5)²

g(x)=(x+5)²

10.

Write the equation of the quadratic function that has a vertex of (-5, 9) and passes through the point (-7, -15).

y = 6(x + 5)² + 9

y = -6(x - 5)² + 9

y = 6(x - 5)² + 9

y = -6(x + 5)² + 9

11.

Write the equation of the quadratic function that has a x-intercepts at (2, 0) and (4, 0) and passes through the point (3, 4).

y = -4(x - 2)(x - 4)

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

y = 4(x - 2)(x - 4)

y = -0.25(x - 2)(x - 4)

12.

Which of the following is the correct equation for the given graph?

y > -x² + 8x - 15

y > -x² - 2x + 3

y < x² - 8x + 17

y > x² + 8x + 17

13.

Which of the following is the correct inequality for the given graph?

y ≥ -(x + 4)² + 1

y < -(x - 4)² + 1

y ≤ (x - 4)² + 1

y ≤ -(x - 4)² + 1

14.

Which of the following is the correct inequality for the given graph?

y < x² - 4x + 4

y > x² - 4x +4

y ≥ x² + 4x + 4

y ≤ x² + 4x + 4

15.

Which of the following is the correct equation for the given graph?

y = -2x² + 12x - 20

y = 2x² + 8x + 5

y = 2x² - 8x + 5

y = -2x² + 8x - 11

16.

Which of the following is the correct equation for the given graph?

y = 2x² - 8x + 12

y = -2x² + 8x - 4

y = 2x² + 8x + 12

y = 2x² + 16x + 30

17.

Which of the following is the correct equation for the given graph?

f(x) = x² - 4x + 3

f(x) = x² + 4x + 3

f(x) = -x² - 4x - 5

f(x) = -x² + 4x - 5

18.

Find the axis of symmetry

x = -¼ (y + 6)² - 1

x = -1

x = 1

y = 6

y = -6

19.

Find the axis of symmetry

f(x)= -2x²- 16x + 3.

x = -8

x = 8

x = 4

x = -4

20.

Find the axis of symmetry

f(x) = -2(x + 2)(x - 4)

x = -2

x = 1

x = 4

x = 18

21.

Find the vertex

f(x) = - (x + 5)(x - 1)

(5, -1)

(-5, 1)

(-2, 9)

(2, -7)

22.

Find the vertex

y = 3(x + 5)² - 4

(5, -4)

(-5, -4)

(-15, -4)

(15, -4)

23.

Find the vertex

y = 2x²+ 8x + 20

(-2, 12)

(-2, 20)

(4, 104)

(-4, 20)

24.

What is the equation in vertex form?

y = -4(x + 3)² - 4

y = -4(x - 3) - 4

y = -4(x + 3)² + 4

y = -4(x - 3)² + 4

25.

Given the zeros below, what is the quadratic equation?

y=x² +9x -8

y=x² +9x +8

y=x² -9x -8

y=x² -9x-8

26.

Write the equation of the quadratic function that has a vertex of (4,-1) and passes through the point (8, 3).

y = 1/4(x - 4)² - 1

y = 4(x - 4)² - 1

y = 4(x + 4)² - 1

y = 1/4(x + 4)² - 1

27.

Transfer from Standard Form to Vertex Form: n² - 4n - 15 = 6

(n - 2)² - 25

(n + 2)² +25

(n - 2)² - 13

(n - 2)² + 13

28.

Convert to vertex form.
y = 3x² +6x - 5

y=3(x+1)² - 8

y=3(x-1)² - 8

y=3(x+2)² - 8

y=3(x-2)² - 8

29.

What is the equation of the table?

y=-5x+10

y=x² - 5x + 6

y=-5x² + 10x + .89

30.

Which quadratic function best represents the graph that has x-intercepts at 9 and 1 and passes through the point (0, -18)?

y = x² + 9x - 18

y = -2(x - 9)(x - 1)

y = -2(x + 9)(x + 1)

y = 2(x + 9)(x + 1)

31.

Which quadratic function in vertex form best represents the graph that has a vertex at (4,-1) and passes through the point (8, 3)?

f(x) = 1/4(x - 4)² - 1

f(x) = 4(x - 4)² - 1

f(x) = 4(x + 4)² - 1

f(x) = 1/4(x + 4)² - 1

32.

Which quadratic equation best represents the graph that has a y-intercept of (0, -6)?

y = -(x - 1)(x - 6)

y = (x + 1)(x + 6)

y = -(x + 1)(x + 6)

y = -6(x + 1)(x + 6)

33.

A quadratic equation has a vertex form of y = -2(x - 1)² - 2. Which of the following is equivalent to this form?

y = 2x² - 4x + 4

y = -2x² + 4x - 4

y = -2x² - 4x + 4

y = 2x² + 4x - 4

34.

Write the explicit function for the given quadratic table.

f(x)=2x²+3x-5

f(x)=2x²+4x-1

f(x)=x²+2x

f(x)=x²+4x+0

35.

Write the explicit function for the given quadratic table.

f(x)=3x²+1x+2

f(x)=3x²-3x+6

f(x)=6x²+2x-2

f(x)=x²+4x+1

36.

Write the explicit function for the given quadratic table.

f(x)=x²-5x+7

f(x)=2x²-3x+2

f(x)=x²-1x+3

f(x)=x²+4x+1

37.

Find the quadratic function with vertex (2, 0) and passing through (1, 3).

y = 3x² + 12x - 12

y = - 3x² + 6x - 1

y = 3x² - 12x + 12

y = 3x² - 6x + 9

38.

Find the quadratic function passing through the points (0, -3), (1, 2), and (2, -1).

y = - x² + 2x - 3

y = x² - 2x + 3

y = x² - 3

y = - x² + 3

39.

Write the equation of the parabola shown.

y = 2x² + 4x - 5

y = 2x² - 4x + 5

y = 2x² + 4x + 5

y = 2x² - 4x - 5

40.

Write the equation of the parabola that has vertex (0, 0) and directrix y = ¹/₄. Then find the value of the function when x = ³/₂.

y = - ⁹/₄

y = ⁹/₄

y = - ⁹/₁₆

y = ⁹/₁₆

41.

Write the equation of the parabola that has vertex (-1, 3) and directrix y = 5.

y = - ¹/₈x² + ¹/₂x - ¹⁵/₈

y = - ¹/₈x² - ¹/₂x + ¹⁵/₈

y = - ¹/₈x² - ¹/₄x + ²³/₈

y = - ¹/₈x² - ¹/₄x - ²³/₈

42.

Write the equation of the parabola that vas vertex (-1, 3) and directrix y = 5. Then find the value of the function when x = -9.

y = - 16

y = - 7.5

y = - 5

y = - 10.75

43.

Write the equation of a parabola that has vertex (2, 1) and focus (2, 4).

y = ¹/₁₂x² - ¹/₃x - ⁴/₃

y = ¹/₁₂x² + ¹/₃x + ⁴/₃

y = ¹/₁₂x² + ¹/₃x - ⁴/₃

y = ¹/₁₂x² - ¹/₃x + ⁴/₃

44.

Write the equation of the parabola that has focus (2, 2) and directrix y = -2. Then find the value of the function when x = -14.

y = 31

y = 32

y = 28.25

y = 27.25

45.

What is the YELLOW point called?

Vertex

Focus

Directrix

Axis of Symmetry

46.

What is the YELLOW line called?

Vertex

Focus

Directrix

Axis of Symmetry

47.

What is the BLUE point called?

Vertex

Focus

Directrix

Axis of Symmetry

48.

Y = ax² + bx + c is called the ______________ form of a quadratic equation.

Vertex

Intercept

Standard

Usual

49.

Y = a(x-h)² + k is called the ______________ form of a quadratic equation.

Vertex

Intercept

Standard

Usual

50.

The values of x that make a quadratic equation ax²+ bx + c =0 true are called __________.

Solutions

Roots

Zeros

All of these

51.

The parabola shown has ____ solution(s).

52.

A parabola is the set of all points that are equidistant from a _____ and a _____ not on the _____.

line, point, line

point, line, point

curve, point curve

point, curve, point

53.

Write an equation in Standard Form

54.

Write an equation in Standard Form

55.

Write an equation in Standard Form

56.

Write an equation in vertex form

57.

Write an equation in vertex form

58.

Write an equation in vertex form

59.

Write the equation in (h, k) form

60.

Write the equation in vertex form:

61.

Write the equation in vertex form:

62.

Graph the equation

63.

Graph the equation

64.

Graph the equation

65.

Graph the equation

66.

Graph the equation

67.

Graph the equation

68.

Graph the equation

69.

Graph the equation

70.

Graph the equation

71.

Convert from Standard Form to Vertex form: m² + 10m + 16 = 0

(m - 5)² - 9

(m + 5)² - 9

(m - 5)² + 9

(m + 5)² + 9

72.

Transfer from Standard Form to Vertex Form: x² - 12x - 64 = 0

(x - 6)² - 28

(x - 6)² - 100

(x - 6)² + 28

(x - 6)² + 100

73.

Does the equation open or or down?
Y = -3x² +7x - 2

down

74.

What is the vertex ?

(0, 7)

(6, 7)

(3,3)

(3,1)

75.

What is the vertex?

(-3, 1)

(-1, 4)

(0, 3)

(-3, 0)

76.

What is the Axis of Symmetry? select all that apply

half way between the zeros

the y-intercept

the x-value of the vertex

the y-value of the vertex

77.

Which of the parabolas have x=1 as the axis of symmetry?

78.

what is the y-intercept of the parabola?

y =1

y = -7

y = 3

y = 7

79.

What is the zeros of the equation: y = 2(x - 7)(x + 3)

-7, 3

7, -3

-2

80.

What are the linear factors if the zeros (roots) are -4 and 5?

(x + 4) (x - 5)

(x - 4) (x + 5)

(x + 4) ( x + 5)

(x - 4) (x - 5)

81.

Given: vertex (1, 18) and zeros -2 and 4 What is the equation of the quadratic function in factored form?

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

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

y = 1/2 (x+ 2) (x - 4)

y = -1/2 ( x + 2) ( x - 4)

82.

which of the following would be the linear factors of the quadratic function?

y = a (x - 3)(x + 1)

y = a (x - 3) (x - 1)

y = a (x + 3)(x - 1)

y = a(x+ 3)(x + 1)

83.

Given the parabola has the zeros of -10 and 4 what is the axis of symmetry?

x = 3

x = 1/3

x = -3

x = - 1/3

84.

When given the zeros, how do you find the vertex?

First find the axis of symmetry then plug that into the equation for x and solve for y.

First plug the zeros into the equation for x and solve

guess

First find the axis of symmetry then plug that into the equation for y and solve for x.

85.

What is the equation of the parabola?

y =(x - 1)(x-3)

y = -1/2(x - 1)(x + 3)

y = 2(x + 1)(x - 3)

y = - 1(x- 1)(x - 3)

86.

what is true about the quadratic Function, f(x) =2(x + 4)(x - 2).

I. The zeros for the function are 4 and -2

II. The axis of symmetry is x = 2.

III. The y-intercept is the point (0, -16)

I only

II only

III only

I and II

I , II, and III

87.

Does the quadratic function have a max or min y = -2(x - 2) (x + 4) what is the point?

maximum (-1, -12)

minimum (-1, 18)

maximum (-1, 18)

minimum (1, -12)

88.

Is the graph of the quadratic equation concave up or concave down? Explain why.... y = 4(x - 3)(x + 5)

concave up because the vertex is positive

concave down because "a" is negative

concave down because the roots are positive

concave up because "a" is positive

89.

If a = -1/2 which of the following might be the graph to match the quadratic equation?

90.

Which number in the quadratic function determines the concavity of the parabola?... y = 3(x - 2)(x + 8)

-8

91.

What is the equation of the parabola in factored form?

y = -4(x + 3)(x - 1)

y = -1(x + 3)(x - 1)

y = 0(x - 3)(x + 1)

y = -4(x - 3)(x + 1)

92.

What are the zeros of the quadratic equation, y = -2(x + 8)(x + 3)?

8, 3

8, -3

-2, -8, -3

-8, -3

93.

Identify the vertex and whether the graph opens up or down.

(5, 2); opens up

(5, 2); opens down

(-5, 2); opens up

(-5, 2); opens down

94.

If given the equation
y = 3(x + 5)² - 4,
what is the vertex of the parabola?

(5, -4)

(-5, -4)

(-15, -4)

(15, -4)

95.

What is the axis of symmetry for this graph?

y=2

x=2

x=0

y=0

96.

What do we call the highest or lowest point of a quadratic?

parabola

vertex

graph

point

97.

What function has a vertex of (-6,4) and passes through (-5,0)?

y = -4(x + 6)² + 4

y = -2(x - 6)² + 4

y = 3(x + 6)² + 4

y = -(x - 6)² + 4

98.

What function has a vertex of (-2,-5) and passes through (0,7)?

y = 3(x + 2)² - 5

y = 5(x + 2)² - 5

y = 4(x - 2)² + 5

y = 2(x + 2)² + 5

99.

100.

What is the vertex form for a vertex of (-3,-5) and when a=-2?

y = -2(x-3)²+5

y = -2(x+3)²+5

y = -2(x+3)²-5

101.

What is the axis of symmetry of the given function?

y = 1

y = -1

x = 1

x = -1

102.

Identify the vertex and whether the graph opens up or down.

(-1, 4); opens up

(-1, 4); opens down

(1, 4); opens up

(1, 4); opens down

103.

Which equation has a vertex of (-3, 4)?

y = 2(x+3)²+ 4

y = (x+3)² - 4

y = (x-3)² + 4

y = 2(x - 3)² + 4

104.

If the a value is negative, which direction does the parabola open?

down

left

right

105.

What is the Vertex coordinates for the following parabola: 2(x-3)²+4
Hint: vertex formula is a(x-h)²+k

(2,4)

(3,4)

(1,4)

(0,2)

106.

Which of the following equations is a parabola?

y = 2x + 4

y = 2x³ + 4

y = 2x²+ 4

y = 2^x

107.

Which is the most basic equation, or parent function, of a parabola?

y = x²

y = 2x² + 3

y = -x² -4

y = -x²

108.

What happens to the parabola when you multiply its equation by a number bigger than 1?
In other words, |a|>1?

Graph moves UP

Graph gets WIDER

Graph moves DOWN

Graph gets NARROWER

109.

Which of the following will be a parabola that opens down?

y = x² -1

y = -x²

y = -x -1

y = 3x²

110.

What is the turning point of this graph?

x=2

y=-3

(2, 1)

y=1

111.

What are the coordinates of the y-intercept?

(-3, 0)

(0, -3)

(2, 1)

y=-3

112.

What are the x-intercepts for this graph?

1 and 3

1 and -3

0 and -3

0 and 3

113.

Does this graph show a maximum or a minimum?

Maximum

Minimum

114.

In vertex form, y= a(x-h)²+k, what effect does the k have on the graph?

Translates vertically

Translates horizontally

Dilates (stretches)

Reset

Unit 2 Quadratics Writing & Transformations

Total questions: 114

Worksheet time: 8hrs 51mins

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