Free Printable Graphing Quadratics

1.

Which equation is Vertex Form?

a)

y=ax²+bx+c

b)

y=a(x-h)²+k

2.

Which equation is in standard form?

a)

y=a(x-h)²+k

b)

y=ax²+bx+c

3.

Given the equation for this parabola:
y=-(x-4)²-3,
does this parabola have a maximum or minimum value?

a)

Maximum

b)

Minimum

4.

What is the vertex of this quadratic equation?

y = 2(x + 2)² + 5

a)

(-2,5)

b)

(2,5)

c)

(5,-2)

d)

(-5,-2)

5.

a)

y=(x-4)²+1

b)

y=(x-4)²-1

c)

y=(x+4)²+1

d)

y=(x+4)²-1

6.

Which equation matches the graph?

a)

y=(x-2)²+3

b)

y=(x-2)²-3

c)

y=(x+2)²+3

d)

y=(x+2)²-3

7.

Where is the axis of symmetry for this parabola?

a)

x = −1

b)

x = 0

c)

y = 3

d)

x = −3

8.

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

a)

x = -4

b)

x = 4

c)

y = 4

d)

y = -4

9.

What is the axis of symmetry?
y = 3x²- 6x + 4

a)

x=1

b)

x=-6

c)

x=2

d)

x=-1

10.

What is the vertex?
f(x) = 2(x - 5)² + 12

a)

(-5, -12)

b)

(5,-12)

c)

(5, 12)

d)

(-5, 12)

11.

Find the Vertex: y= -5x²-20x - 26

a)

(-2, -6)

b)

(2, 6)

c)

(6,2)

d)

(3, 6)

12.

What is the vertex?
f(x) = -x²- 4x + 12.

a)

(-2, 16)

b)

(2, 0)

c)

(2, 4)

d)

(-2, 4)

13.

What is the vertex?
y = -2x² + 4x + 3

a)

(0, 3)

b)

(-1, 5)

c)

(1, 5)

d)

(1, -5)

14.

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

a)

(5, -4)

b)

(-5, -4)

c)

(-15, -4)

d)

(15, -4)

15.

What is the range of the function graphed above?

a)

y ≥ -2

b)

y ≤ 4

c)

y ≥ 4

d)

y ≤ -2

16.

What is the range of the parabola above?

a)

y ≤ 2

b)

y ≥ 2

c)

y ≤ 3

d)

y ≥ 3

17.

What is the equation for axis of symmetry?

a)

y=3

b)

x=3

c)

x=5

d)

x=1

18.

What are the green dots called?

a)

axis of symmetry

b)

vertex

c)

parabola

d)

roots or x-intercepts

19.

What is the green dot on the parabola called?

a)

maximum

b)

minumum

c)

roots

d)

zeros

20.

Does this parabola have a maximum or minimum?

a)

Maximum

b)

Minimum

21.

Find the y-intercept of f(x) = 2x²- 2x + 1

a)

2

b)

-2

c)

1

d)

-1

22.

What is the vertex of the quadratic function:
y = x² - 6x + 11?

a)

(3,2)

b)

(-3,-2)

c)

(-3,2)

d)

(3,-2)

23.

Determine the vertex of the parabola:
y = 5x²- 20x + 13

a)

(5, -7)

b)

(-2, -7)

c)

(2, -7)

d)

(-7, -2)

24.

The axis of symmetry line passes through which point?

a)

y-intercept

b)

any random point

c)

vertex

d)

none of these

25.

What are the x- intercepts?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

26.

What is the vertex?

a)

(2, 4)

b)

(3, -1)

c)

(0, 8)

d)

(4, 2)

27.

Factor
n²-13n+40

a)

(n-5)(n-8)

b)

(n+5)(n-8)

c)

(n-5)(n+8)

d)

(n+6)(n+1)

28.

Which equation is graphed above?

a)

$y=-\left(x-1\right)^2+4$

b)

$y=\left(x-1\right)^2+4$

c)

$y=-\left(x-4\right)^2+1$

d)

$y=\left(x-4\right)^2+1$

29.

Which equations matches the graph above?

a)

$h\left(x\right)=\ \left(x+1\right)^2-4$

b)

$h\left(x\right)=-\left(x+1\right)^2-4$

c)

$h\left(x\right)=\left(x+4\right)^2-1$

d)

$h\left(x\right)=-\left(x+4\right)^2+1$

30.

$f\left(x\right)=-\left(x-4\right)^2+1$

Choose the correct graph of the equation.

a)

b)

c)

d)

31.

Which equation matches the graphed above?

a)

$p\left(x\right)=\left(x-1\right)^2+4$

b)

$p\left(x\right)=\left(x-4\right)+1$

c)

$p\left(x\right)=-\left(x+1\right)^2-4$

d)

$p\left(x\right)=-\left(x+4\right)\ ^2-1$

32.

Which equation matches the graph above?

a)

$r\left(x\right)=-\left(x+4\right)^2-1$

b)

$r\left(x\right)=\left(x+4\right)^2-1$

c)

$r\left(x\right)=-\left(x-4\right)^2+1$

d)

$r\left(x\right)=\left(x-4\right)^2+1$

33.

Which equation matches the graph?

a)

$f\left(x\right)=\left(x-1\right)^2+4$

b)

$f\left(x\right)=\left(x+4\right)^2-1$

c)

$f\left(x\right)=-\left(x-1\right)^2+4$

d)

$f\left(x\right)=-\left(x+4\right)^2-1$

34.

What is the vertex of the following equation? $f\left(x\right)=-\frac{1}{2}\left(x-5\right)^2+6$

a)

$\left(-5,-6\right)$

b)

$\left(-5,6\right)$

c)

$\left(5,-6\right)$

d)

$\left(5,6\right)$

35.

What piece of information does h identify in the following equation?
y=a(x-h)²+k

a)

y value of the vertex

b)

Axis of Symmetry

c)

Direction (facing up or down)

d)

x-intercept

36.

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

a)

(5, -4)

b)

(-5, -4)

c)

(-15, -4)

d)

(15, -4)

37.

Given the equation for this parabola:
y=-(x-4)²-3,
does this parabola have a maximum or minimum value?

a)

Maximum

b)

Minimum

c)

Not enough information

38.

What is the axis of symmetry for the following quadratic function: f(x)=1/2(x-4)²+3

a)

x=4

b)

x=-4

c)

x=1/2

d)

x=3

39.

What is the vertex of the parabola: y=2(x-3)²+4

a)

(3,4)

b)

(-3,4)

c)

(3, -4)

d)

(-3,-4)

40.

What causes the graph of y = x² to open downward?

a)

multiply the x² by a fraction

b)

multiply the x² by a decimal

c)

multiply the x² by a negative number

d)

multiply the x² by a number greater than 1

41.

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

a)

(5, 2); opens up

b)

(5, 2); opens down

c)

(-5, 2); opens up

d)

(-5, 2); opens down

42.

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

a)

f(x) = -(x + 2)² - 4

b)

f(x) = -(x - 2)² - 4

c)

f(x) = -3(x - 2)² - 4

d)

f(x) = -3(x + 2)² - 4

43.

What are the green dots called?

a)

axis of symmetry

b)

vertex

c)

parabola

d)

roots or x-intercepts

44.

What is the green dot on the parabola called?

a)

maximum

b)

minumum

c)

roots

d)

zeros

45.

The axis of symmetry line passes through which point?

a)

y-intercept

b)

any random point

c)

vertex

d)

symmetrical point for the vertex

46.

What is the green dashed line called?

a)

roots or x-intercepts

b)

parabola

c)

axis of symmetry

d)

line of dashes

47.

Which variable, when negative, can cause the parent function to reflect across the x-axis (face downwards)?

a)

a

b)

h

c)

k

48.

Compared to the parent function, f(x) = x², which of the following is the equation of the function after a vertical stretch by a factor of 3?

a)

A

b)

B

c)

C

d)

D

49.

Compared to the parent function, f(x) = x², which of the following is the equation of the function after a vertical shrink by a factor of 1/3?

a)

A

b)

B

c)

C

d)

D

50.

af(x) is a...

a)

Vertical translation

b)

Horizontal stretch/compression

c)

Horizontal translation

d)

Vertical stretch/compression

51.

Vertical stretch is af(x) when...

a)

a is greater than 0

b)

a is less than 0

c)

a is greater than 1

d)

a is a fraction/decimal

52.

Vertical compression is af(x) when a is...

a)

a fraction/decimal and the graph flattens

b)

a number greater than 1 and the graph becomes steeper

c)

any type of number

d)

any number less than 1

53.

f(x-c)

a)

slides left

b)

slides right

c)

slides up

d)

slides down

54.

Vertical translation

a)

af(x)

b)

f(x-c)

c)

f(x)+d

d)

f(bx)

55.

Describe the transformation that occurred
3f(x)

a)

Up 3 units

b)

Narrower / Steeper

c)

Wider / Less Steep

d)

Right 3 units

56.

Match the equation to its description.

a)

Vertical Stretched by 2 and translation up 4

b)

Vertical Compressed by 2 and translation up 4

c)

Horizontal Stretched by 2 and translation left 4

d)

Horizontal Compressed by 2 and translation right 4

57.

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

58.

Does the equation vertically stretch, compress, or reflect?

f\left(x\right)=0.75x^2

*Always compare to the parent function (graph first)*

a)

Stretch by a factor of 2

b)

Compress by a factor of 0.75

c)

Reflect across the x-axis

d)

Both stretch by a factor of 2 and reflect across the x-axis

59.

Does the equation vertically stretch, compress, or reflect?

f\left(x\right)=\ 2x^2

*Always compare to the parent function (graph first)*

a)

Stretch by a factor of 2

b)

Compress by a factor of 2

c)

Reflect across the y-axis

d)

Both Stretch by a factor of $\frac{1}{2}$ & Reflect across the x-axis

60.

Does the equation vertically stretch, compress, or reflect?
$f\left(x\right)=-x^2$
*Always compare to the parent function (graph first)*

a)

Stretch by a factor of 2

b)

Compress by a factor of $-2$

c)

Reflect across the x-axis

d)

Both Compress by 2 and Reflect across the x-axis

61.

Does the equation vertically stretch, compress, or reflect?
$f\left(x\right)=-5x^2$
*Always compare to the parent function (graph first)*

a)

Stretch by a factor of 5

b)

Compress by a factor of $\frac{5}{2}$

c)

Reflect across the x-axis

d)

Both Stretch by a factor of 5 & Reflect across the x-axis

62.

Does the equation vertically stretch, compress, or reflect?
$f\left(x\right)=\frac{1}{4}x^2$
*Always compare to the parent function (graph first)*

a)

Stretch by a factor of $\frac{1}{4}$

b)

Compress by a factor of $\frac{1}{4}$

c)

Reflect across the x-axis

d)

Both Compress by a factor of 2 & Reflect across the x-axis

63.

Does the equation vertically stretch, compress, or reflect?
$f\left(x\right)=0.5x^2$
*Always compare to the parent function (graph first)*

a)

Stretch by a factor of 0.5

b)

Compress by a factor of 0.5

c)

Reflect across the x-axis

d)

Both Compress by a factor of 0.5 & Reflect across the x-axis

64.

Does the equation vertically stretch, compress, or reflect?
$f\left(x\right)=10x^2$
*Always compare to the parent function (graph first)*

a)

Stretch by a factor of 10

b)

Compress by a factor of 2

c)

Reflect across the x-axis

d)

Both Compress by a factor of 10 & Reflect across the x-axis

65.

Does the equation vertically stretch, compress, or reflect?
$f\left(x\right)=-7x^2$
*Always compare to the parent function (graph first)*

a)

Stretch by a factor of 7

b)

Compress by a factor of $-7$

c)

Reflect across the x-axis

d)

Both Stretch by a factor of 7 & Reflect across the x-axis

66.

Does the equation vertically stretch, compress, or reflect?
$f\left(x\right)=\frac{1}{7}x^2$
*Always compare to the parent function (graph first)*

a)

Stretch

b)

Compress

c)

Reflect

d)

Both Compress & Reflect

67.

What is the parent function of a quadratic?

a)

$y=x^2$

b)

$y=x$

c)

$y=\sqrt{x}$

d)

$y=\left|x\right|$

68.

Identify the steps for identifying the translations of quadratic functions.

a)

Graph the parent function

b)

Solve for y

c)

Solve for x

d)

Graph the given equation

69.

What do we call the graph of a quadratic?

a)

line

b)

vertex

c)

equation

d)

parabola

70.

What is the green dot on the parabola called?

a)

maximum

b)

minumum

c)

roots

d)

zeros

71.

Does this parabola have a maximum or minimum?

a)

Maximum

b)

Minimum

72.

The axis of symmetry line passes through which point?

a)

y-intercept

b)

any random point

c)

vertex

d)

none of these

73.

What is the vertex?
f(x) = -x²- 4x + 12.

a)

(-2, 16)

b)

(2, 0)

c)

(2, 4)

d)

(-2, 4)

74.

What are the coordinates of the vertex? Is it a maximum or a minimum?

a)

(2, 3); minimum

b)

(2, 5); maximum

c)

(2, 3); maximum

d)

(2, -3); minimum

e)

(2, -3); maximum

75.

Determine the vertex of the parabola:
y = 5x²- 20x + 13

a)

(5, -7)

b)

(-2, -7)

c)

(2, -7)

d)

(-7, -2)

76.

Find the Vertex: y= -5x²-20x - 26

a)

(-2, -6)

b)

(2, 6)

c)

(6,2)

d)

(3, 6)

77.

Graph the quadratic.

a)

A

b)

B

c)

C

d)

D

78.

Graph the quadratic.

a)

A

b)

B

c)

C

d)

D

79.

What is the vertex of y= x²- 8x + 14 ?

a)

(2, 4)

b)

(-4, -2)

c)

(4, -2)

d)

(-2, 4)

80.

Find the vertex of the quadratic:
y = -2x² + 4x + 3

a)

(0, 3)

b)

(-1, 5)

c)

(1, 5)

d)

(1, -5)

81.

a)

A

b)

B

c)

C

d)

D

82.

a)

A

b)

B

c)

C

d)

D

83.

a)

A

b)

B

c)

C

d)

D

84.

a)

A

b)

B

c)

C

d)

D

85.

a)

A

b)

B

c)

C

d)

D

86.

a)

A

b)

B

c)

C

d)

D

87.

Which is the vertex of y = x²+ 16x + 71 ?

a)

V(-8, 7)

b)

V(-8, 3)

c)

V(8, 10)

d)

V(16, -2)

88.

Find the y-intercept y = x² - 6x + 5

a)

(0, 8)

b)

(0, - 6)

c)

(5, 0)

d)

(0, 5)

89.

Find the y-intercept of f(x) = 2x²- 2x + 1

a)

(1,0)

b)

(-2,0)

c)

(0,1)

d)

(0, -1)

90.

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

a)

up

b)

down

c)

Neither; it opens to the right.

d)

Neither; it opens to the left.

91.

What is the name of this form:
y = ax² + bx + c

a)

vertex form

b)

standard form

c)

factored form

d)

zero form

92.

What is the vertex of this parabola?

a)

(−1, 3)

b)

(−3, 11)

c)

(−2, 5)

d)

(0, 5)

93.

What is the y-intercept of this parabola?

a)

(−1, 3)

b)

(−3, 11)

c)

(−2, 5)

d)

(0, 5)

94.

Where is the axis of symmetry for this parabola?

a)

x = −1

b)

x = 0

c)

y = 3

d)

x = −3

95.

What is the vertex?
y = -2x² + 4x + 3

a)

(0, 3)

b)

(-1, 5)

c)

(1, 5)

d)

(1, -5)

96.

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

a)

x = -4

b)

x = 4

c)

y = 4

d)

y = -4

97.

What is the axis of symmetry?
y = 3x²- 6x + 4

a)

x=1

b)

x=-6

c)

x=2

d)

x=-1

98.

What is the vertex?
f(x) = -x²- 4x + 12.

a)

(-2, 16)

b)

(2, 0)

c)

(2, 4)

d)

(-2, 4)

99.

What is the y-intercept?
f(x) = -2x² + 4x - 6

a)

(0, 6)

b)

(0, -6)

c)

(6, 0)

d)

(-6, 0)

Graphing Quadratics

Total questions: 99

Worksheet time: 4hrs 51mins

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