Free Printable EXTRA PRACTICE: Graph Characteristics/Transformations Quadratic

1.

Is this a max or min?

a)

max

b)

min

c)

cannot be determined

2.

A line about which a figure is symmetric is the:

a)

Solution Set

b)

Intercept Formula

c)

Quadratic Function

d)

Axis of Symmetry

3.

What is the Axis of symmetry?

a)

Y=3

b)

y=-3

c)

x= 3

d)

x=-3

4.

What is the significance of the ordered pair (2, -4) to the graph?

a)

It is the vertex

b)

It is an x-intercept

c)

It is the y-intercept

d)

It is the axis of symmetry

5.

Determine the domain and range of the function

a)

Domain: All real numbers, Range: All real numbers

b)

Domain: x ≥ -4, Range: All real numbers

c)

Domain: All real numbers, Range: y ≥ -4

d)

Domain: -1 ≤ x ≤ 5, Range: y ≥ -4

6.

Quadratic equations take the shape of a _______ when graphed.

a)

parabola

b)

straight line

c)

snaked line

d)

elliptical

7.

Use the picture to find the vertex and axis of symmetry

a)

Vertex (3,8) Axis x=3

b)

Vertex (3,8) Axis y=3

c)

Vertex (8,3) Axis x=3

d)

Vertex (8,3) Axis y=3

8.

State the vertex of the graph whose function is $f\left(x\right)=\left(x-4\right)^2+8$

a)

(4,8)

b)

(4, -8)

c)

(-4, 8)

d)

(-4, -8)

9.

Does the following graph of the quadratic have a maximum or minimum: $y=-3\left(x+4\right)^2+7$

a)

maximum

b)

minimum

c)

neither

d)

both

10.

State the axis of symmetry $y=-3\left(x+4\right)^2+7$

a)

$x=4$

b)

$y=4$

c)

$x=-4$

d)

$y=-4$

11.

What is the green dot on the parabola called?

a)

maximum

b)

minumum

c)

roots

d)

zeros

12.

What is the range of this parabola?

a)

All real #'s

b)

y > -1

c)

y < -1

d)

x > -4

13.

Does the parabola
f(x)=4(x-2)² + 3
open up or down?

a)

up

b)

down

14.

What is the equation of this graph?

a)

f(x) = (x -5)² + 1

b)

f(x) = (x - 1)² - 5

c)

f(x) = (x + 1)² - 5

d)

f(x) = (x + 5)² +1

15.

Factor x² + 7x + 12
What two numbers ADD UP TO 7
and MULTIPLY to 12.

a)

(x + 2)(x + 5)

b)

(x + 3)(x + 4)

c)

(x + 1)(x + 6)

16.

Factor x² + 12x + 20
WHAT TWO NUMBERS MULTIPLY TO 20
AND ADD UP TO 12?

a)

(x + 2)(x + 10)

b)

(x + 7)(x + 5)

c)

(x + 6)(x + 6)

17.

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 and the x coordinate of the vertex

c)

Direction (facing up or down)

d)

x-intercept

18.

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

19.

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

20.

Which of the following is a transformation of the graph y = 3x².

a)

Shifts up 3.

b)

Shifts left 3.

c)

Vertical stretch by a factor of 3.

d)

Shifts right 3.

21.

Using the graph of the quadratic function, identify the y-intercept.

a)

(4, -6)

b)

(0, 2)

c)

(.5, 0)

d)

(7.5, 0)

22.

Using the graph of the quadratic function, identify the vertex.

a)

(4, -6)

b)

(0, 2)

c)

(.5, 0)

d)

(7.5, 0)

23.

What is Standard form?

a)

$y=ax^2+bx+c$

b)

$y=a\left(x-p\right)\left(x-q\right)$

c)

$y=a\left(x-h\right)^2+k$

d)

$y=mx+b$

24.

x-intercepts are also known as...

a)

Zeros

b)

Roots

c)

Solutions

d)

I have no idea what you are talking about

25.

Find the zeros.

a)

0 and 4

b)

0 and -4

c)

0

d)

-4

26.

A parabola has a vertex at (-3,2). Where is the axis of symmetry?

a)

y = -2

b)

x = 3

c)

x = -3

d)

y = 2

27.

What is the axis of symmetry for the following equation?

y=4x²-8x+9

a)

x=-8

b)

x=1

c)

x=-1

d)

x=2

28.

Does this graph in the back have maximum or minimum value?

a)

maximum

b)

minimum

c)

neither

d)

both

29.

The two solutions to
y = 2x² -x -3 are...

a)

1 and 3/2

b)

-1 and 3/2

c)

-1 and -3/2

d)

1 and -3/2

30.

Identify where the function is decreasing.

a)

$\left(-\infty,0\right)$

b)

$\left(0,\infty\right)$

c)

$\left(-\infty,\infty\right)$

d)

$\left(-3,3\right)$

31.

Identify where the function is increasing.

a)

$\left(-\infty,0\right)$

b)

$\left(0,\infty\right)$

c)

$\left(-\infty,\infty\right)$

d)

$\left(-3,3\right)$

32.

Determine if the function graphed has a maximum or a minimum value and identify that value.

a)

maximum at -1

b)

minimum at -1

c)

maximum at 4

d)

minimum at 4

33.

What is the direction of the following graph?

a)

Increasing

b)

Decreasing

c)

Constant

d)

Not a function

34.

Describe the end behavior of the graph.

a)

x → ∞, y→ ∞ and
x→ ∞, y→⁻∞

b)

x → ∞, y→ ∞ and
x→⁻∞, y→∞

c)

None of these

d)

x →∞,y→⁻∞ and
x→∞, y→⁻∞

35.

Which one means the function goes down on the left

a)

x →-∞, y→∞

b)

x →-∞, y→-∞

36.

Which one means up

a)

y →-∞

b)

y →∞

37.

Where is the function decreasing?

a)

y≤-1

b)

y≤-1

c)

y≤3

d)

y≥3

38.

Where is the function increasing?

a)

y≤0

b)

y≥0

c)

y≥4

d)

y≤4

39.

The graph of a quadratic function is called a

a)

Parabola

b)

Vertex

c)

Axis of Symmetry

d)

Vertex Form

40.

What divides the parabola into 2 perfect halves?

a)

Axis of Symmetry

b)

Vertex

c)

Axis of Doom

d)

x - intercept

41.

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

a)

parabola

b)

vertex

c)

graph

d)

point

42.

What is the vertex?

a)

(2, 4)

b)

(3, -1)

c)

(0, 8)

d)

(4, 2)

43.

What are the x- intercepts?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

44.

The axis of symmetry of this parabola is...

a)

y = 4

b)

y = -4

c)

x = 4

d)

x = -4

45.

What is the domain of this quadratic function?

a)

All real numbers.

b)

x ≥ 4

c)

x < 2

d)

x ≤ 4

46.

What is the range of this quadratic function?

a)

All real numbers.

b)

y ≥ 4

c)

y < 4

d)

y ≤ 4

47.

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)

48.

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

a)

Maximum

b)

Minimum

49.

In vertex form, what effect does the a have on the graph?

a)

Translates Up/Down

b)

Translates Left/Right

c)

Narrows/Widens Parabola

d)

Flips it

50.

In vertex form, what effect does the h have on the graph?

a)

Translates Up/Down

b)

Translates Left/Right

c)

Narrows/Widens Parabola

d)

Flips it

51.

Which quadratic function is represented by the graph?

a)

y = 2(x - 4)² + 5

b)

y = 2(x + 4)² + 5

c)

y = -2(x - 4)² + 5

d)

y = -2(x + 4)² + 5

52.

How would you describe the translation from f(x)=x² to f(x)=(x-3)² ?

a)

Horizontal translation: three units to the left

b)

Horizontal translation: three units to the right

c)

Vertical translation: three units up

d)

Vertical translation: three units down

53.

Shift f(x)=x² three units to the left and 4 units down

a)

f(x)=(x+3)²-4

b)

f(x)=(x-3)²-4

c)

f(x)=(x+4)²-3

d)

f(x)=(x-4)²-3

54.

How would you describe the translation from f(x)=x² to f(x)=x²+5 ?

a)

Horizontal translation: five units to the right

b)

Horizontal translation: five units to the left

c)

Vertical translation: five units up

d)

Vertical translation: five units down

55.

What is the axis of symmetry of the graph?

a)

$x=-2$

b)

$x=4$

c)

$y=-2$

d)

$y=4$

56.

What is the vertex of the graph?

a)

$\left(-2,\ 4\right)$

b)

$\left(4,\ -2\right)$

c)

$\left(2,4\right)$

d)

$\left(4,2\right)$

57.

Does this graph have a maximum or minimum?

a)

Maximum at $\left(-2,4\right)$

b)

Minimum at $\left(-2,\ 4\right)$

58.

What is the range of the graph?

a)

y\le4

b)

$x\le4$

c)

$y\ge4$

d)

$x\ge4$

59.

What is the axis of symmetry of the graph?

a)

x=-2

b)

$x=0$

c)

$y=-2$

d)

$y=0$

60.

What is the vertex of the graph?

a)

\left(-2,0\right)

b)

$\left(0,-2\right)$

c)

$\left(2,0\right)$

d)

$\left(0,2\right)$

61.

Does this graph have a maximum or minimum?

a)

Maximum at $\left(-2,0\right)$

b)

Minimum at $\left(-2,0\right)$

62.

What is the range of the graph?

a)

y\ge0

b)

$x\ge0$

c)

$y\le0$

d)

$x\le0$

63.

What is the axis of symmetry of the graph?

a)

x=-4

b)

$y=-4$

c)

$x=1$

d)

$y=1$

64.

What is the vertex of the graph?

a)

\left(-4,\ 1\right)

b)

$\left(1,-4\right)$

c)

$\left(-4,\ -1\right)$

d)

$\left(-1,\ -4\right)$

65.

Does this graph have a maximum or minimum?

a)

Maximum at

\left(-4,1\right)

b)

Minimum at $\left(-4,1\right)$

66.

What is the range of the graph?

a)

$y\le1$

b)

$x\le1$

c)

$y\ge1$

d)

$x\ge1$

67.

The graph of a quadratic is called a?

a)

curve

b)

circle

c)

line

d)

parabola

68.

What is the significance of the ordered pair (2, -4) to the graph?

a)

It is the vertex

b)

It is an x-intercept

c)

It is the y-intercept

d)

It is the axis of symmetry

69.

Is this a max or min?

a)

max

b)

min

c)

cannot be determined

70.

Using the graph of the quadratic function, identify the y-intercept.

a)

(4, -6)

b)

(0, 2)

c)

(.5, 0)

d)

(7.5, 0)

71.

What is the Axis of symmetry?

a)

Y=3

b)

y=-3

c)

x= 3

d)

x=-3

72.

The axis of symmetry of this parabola is...

a)

y = 4

b)

y = -4

c)

x = 4

d)

x = -4

73.

What form is the following equation written in?
y = 2(x - 2)² + 4

a)

Standard

b)

Vertex

c)

Factored

d)

Hege

74.

What form is the quadratic equation written in?
y = 2x² + 5x + 5

a)

Hege

b)

Vertex

c)

Standard

d)

Factored

75.

What form is the quadratic equation written in?
y = (x - 2)(x + 4)

a)

Factored

b)

Standard

c)

Vertex

d)

Hege

76.

What are the x-intercept(s) for the graph of the function: y = (x - 2)(x + 4)

a)

-2, -4

b)

-2, 4

c)

2, -4

d)

2, 4

77.

What is the y-intercept for the graph of the function: y = (x - 2)(x + 4)

a)

2

b)

-4

c)

-6

d)

-8

78.

What is the y-intercept for the graph of the function: y = x² - 3x - 10

a)

3

b)

-3

c)

-10

d)

10

79.

What is the vertex for the graph of the function? y = -2 (x - 3)² + 4

a)

(3, 4)

b)

(-3, 4)

c)

(-3, -4)

d)

(3, -4)

80.

What is the equation for the axis of symmetry for the graph of the function?
y = (x - 1)² + 9

a)

x = -1

b)

x = 1

c)

x = 9

d)

x = -9

81.

What can we find easily in standard form?

a)

vertex

b)

zeros/x-intercepts

c)

y-intercept

82.

What can we find easily in factored form?

a)

y-intercept

b)

vertex

c)

zeros/x-intercepts

83.

What can we find easily in vertex form?

a)

vertex

b)

y-intercept

c)

zeros/x-intercepts

84.

What is the vertex of y=x²+4x+3?

a)

(2,1)

b)

(-2,1)

c)

(0,0)

d)

(-2,-1)

85.

Find the axis of symmetry of f(x) = -(x + 2)(x - 4)

a)

y = 1

b)

x = 1

c)

y = -1

d)

x = -1

86.

WITHOUT USING DESMOS

If the x intercepts are -3 and 5, which equation in intercept form would represent this?

a)

$y=\left(x+3\right)\left(x-5\right)$

b)

$y=\left(x-3\right)\left(x-5\right)$

c)

$y=\left(x-3\right)\left(x+5\right)$

d)

$y=\left(x+3\right)\left(x+5\right)$

87.

Describe the transformation: y=-3(x-2)²-4.

*Mark all that apply.

a)

reflection across x-axis

b)

VS by factor of 3

c)

VC by factor of 3

d)

down 4

e)

right 2

88.

y=(x+2)²+4

*Mark all that apply.

a)

reflection across x-axis

b)

left 2

c)

up 4

d)

right 2

89.

y=-2(x+5)²

*Mark all that apply.

a)

right 5

b)

left 5

c)

VC by a factor of 2

d)

reflection across x-axis

e)

VS by a factor of 2

90.

y= -(x-11)²+6

*Mark all that apply.

a)

right 11

b)

reflection across x-axis

c)

VC

d)

up 6

91.

y= 1/4x²+8

*Mark all that apply.

a)

VC by a factor of 1/4

b)

up 8

c)

left 8

d)

right 8

92.

y= 5/3(x-7)² - 8

*Mark all that apply.

a)

right 7

b)

up 8

c)

down 8

d)

VS by a factor of 5/3

93.

Write the equation of this transformation: up 8

a)

y=(x+8)²

b)

y= x²+8

c)

y= x²-8

d)

y=8x²

94.

Write the equation of this transformation: reflection across x-axis, left 2, down 5

a)

y= -(x+2)²+5

b)

y= -(x+2)²

c)

y= (x-2)²-5

d)

y= -(x+2)²-5

95.

Write the equation of this transformation: VC by a factor of 1/7 and up 2

a)

y= 7x² + 2

b)

y= (x+1/7)² + 2

c)

y= 1/7x² + 2

d)

y= 1/7x² - 2

96.

Write the equation of this transformation: reflection across x-axis, left 3, up 15

a)

y= -(x+3)²+15

b)

y= -(x+3)² - 15

c)

y= (x+3)²+15

d)

y= -(x+15)²+3

97.

What are the transformations?
y = (x - 2)²+ 4

a)

shift 2 units right
shift 4 units up

b)

shift 2 units left
shift 4 units up

c)

shift 2 units right
shift 4 units down

d)

shift 2 units left
shift 4 units up

98.

Does the following quadratic equation have a maximum or minimum value? How can you tell?
y=x²+2x-3

a)

Minimum value, because the a value is positive

b)

Maximum value, because the b value is positive

c)

Maximum value, because the a value is positive

d)

Minimum value, because the c value is negative

99.

If the blue 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

100.

How did we transform from the parent function?
y = x² + 2

a)

horizontal shift up

b)

vertical shift up

c)

horizontal shift down

d)

vertical shift down

101.

What is the horizontal shift of this equation?
y = -(x + 3)² - 5

a)

left 3

b)

right 3

c)

left 5

d)

right 5

102.

What are the green dots called?

a)

axis of symmetry

b)

vertex

c)

parabola

d)

roots or x-intercepts

103.

Which of the following does NOT contain a REFLECTION of y = x²?

a)

y = -2(x + 5)² + 3

b)

y = (-3x + 5)² + 3

c)

y = (1/2) (x + 5)² + 3

d)

y = -x² + 3

104.

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

a)

a reflection across the line x = -4

b)

a reflection across the line y = -4

c)

a translation shifting f(x) 4 units to the left

d)

a translation shifting f(x) 4 units to the right

105.

How does the graph of f(x) = (x + 3)² + 5 compare to the graph of
g(x) = (x - 1)² - 4. {Hint: Compare their vertexes.}

a)

f(x) is shifted 4 left and 9 up from g(x)

b)

f(x) is shifted 4 to the right and 9 down from g(x)

c)

f(x) is shifted 3 left and 5 up from g(x)

d)

f(x) is shifted 4 left and 9 down from g(x)

106.

What is vertex form of a quadratic function

a)

ax² + bx + c

b)

a(x - h)² + k

c)

y - y₁= m(x - x₁)

d)

Ax + By = C

107.

Does the following function have a maximum or a minimum
f(x) = -2(x+3)² - 5

a)

Maximum

b)

Minimum

108.

What is the y-intercept of the following function?
f(x) = -2x² + 3x - 7

a)

(0, -2)

b)

(0, 3)

c)

(0, -7)

d)

(0, 7)

109.

The standard form of a quadratic function is:

a)

ax² + bx + c

b)

a(x - h)² + k

c)

y - y₁= m(x - x₁)

d)

Ax + By = C

110.

If a is negative in the function, which way does the parabola

a)

up

b)

down

c)

left

d)

right

111.

Does the following function open up or down
1/2(x + 2)² - 3

a)

up

b)

down

c)

left

d)

right

112.

The quadratic parent function is

a)

y = x

b)

f(x) = x

c)

f(x) = x²

d)

y = √x

113.

y = (x + 2)² + 9
This graph shifts...

a)

Left 2, down 9

b)

Left 2, up 9

c)

Right 2, up 9

d)

Right 2, down 9

114.

What is the equation for the axis of symmetry?

a)

y=3

b)

x=3

c)

x=5

d)

x=1

115.

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

a)

f(x) = (x - 2)² - 1

b)

f(x) = (x + 2)² - 1

c)

f(x) = -(x + 2)² - 1

d)

f(x) = -(x - 2)² - 1

116.

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

a)

(5, -7)

b)

(-2, -7)

c)

(2, -7)

d)

(-7, -2)

117.

Identify ALL of the transformations performed on $f\left(x\right)=x^2$ to create the graph of $g\left(x\right)=-\left(x-4\right)^2+2$

a)

reflection

b)

stretch

c)

compress

d)

left 4, up 2

e)

right 4, up 2

118.

a)Vertical Dilation

b)Horizontal Translation

c)Horizontal Dilation

d)Vertical Translation

1

2

3

4

1)

2)

3)

4)

119.

Label the graphs with the correct transformation compared to the parent function f(x)=x^2

a)

left

b)

reflected

c)

right

d)

up

e)

down

1

2

3

4

5

1)

2)

3)

4)

5)

120.

The parent function, f(x), is transformed so that it maps into g(x). Which equation would correctly represent g(x)?

(a)

Choose from the below words

g(x)=f(x - 3)

g(x)=f(x + 3)

g(x)=f(x) + 3

g(x)=f(x) - 2

121.

"a" causes the parabola to vertically (a) when a > 1.

Choose from the below words

stretch

compress

122.

$The\ parent\ function\ f\left(x\right)\ =\ x^2$ has translated by opening (a) and moving (b) and to the (c)

the final equation would look like (d)

Choose from the below words

up 3

down 3

right 1

left 1

downward

upward

$f\ =\ -\left(x-1\right)^2\ +3$

123.

Match each graph with how it would move according to the (h,k) shifts. The original graph is $y=x^2.$ It's graph is on the left.

a)

1.

(h,k) = (2,-3)

b)

2.

(h,k) = (-2,3)

c)

3.

(h,k) = (-3,-2)

124.

"a" causes the parabola to vertically (a) when a < 1.

Choose from the below words

compress

stretch

125.

"b" causes the parabola to horizontally (a) when $b>1$ .

Choose from the below words

compress

stretch

126.

$The\ parent\ function\ f\left(x\right)\ =\ x^2$ has translated by reflecting (a) and moving (b) and to the (c)

the final equation would look like (d)

Choose from the below words

up 3

down 3

right 1

left 1

across x axis

upward

$f\ =\ -\left(x-1\right)^2\ +3$

127.

Identify the possible function that matches each specific transformation listed from the parent function $f\left(x\right)=x^2$

a)

$f\left(x\right)=-x^2+36$

b)

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

c)

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

d)

$f\left(x\right)=-\left(x-7\right)^2$

e)

$f\left(x\right)=\left(x+1\right)^2+5$

f)

$f\left(x\right)=x^2-5$

g)

$f\left(x\right)=-5x^2$

h)

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

1

2

3

4

1)

2)

3)

4)

128.

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

129.

Identify the possible functions that matches each specific transformation listed from the parent function f(x) = x^2

a)

$f\left(x\right)\ =-5x^2$

b)

$f\left(x\right)=\ -\left(x-7\right)^2$

c)

$f\left(x\right)\ =\ x^2-7$

d)

$f\left(x\right)=\ \left(x+1\right)^2+5$

e)

$f\left(x\right)=\ \left(x-1\right)^2+5$

f)

$f\left(x\right)=\ \left(x+1\right)^2-5$

g)

$f\left(x\right)=\ 5x^2$

h)

$f\left(x\right)=\ -\left(x+7\right)^2$

i)

$f\left(x\right)\ -\frac{1}{5}x^2$

1

2

3

4

1)

2)

3)

4)

130.

Match the description to its equation.Moves right 7 (a)

Choose from the below words

A

B

C

D

131.

"b" causes the parabola to horizontally* (a) when $b<1$ .

*TYPO ON PACKET

Choose from the below words

compress

stretch

132.

The graph of quadratic parent function f was transformed to create the graph of e(x). Which two equations represent the translation on the graph? (Place the f(x) version in the second spot).

Choose from the below words

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

$e\left(x\right)=f\left(x\right)\ +\ 3$

$e\left(x\right)=x^2\ -\ 3$

$e\left(x\right)=f\left(x\right)\ -\ 3$

$e\left(x\right)=\left(x\ -\ 3\right)^2$

$e\left(x\right)=f\left(x\ -\ 3\right)$

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

$e\left(x\right)=f\left(x\ +\ 3\right)$

$e\left(x\right)=3f\left(x\right)$

$e\left(x\right)=3x^2$

133.

Label how each number transforms the function

a)

Left 3

b)

Moves up 7

c)

Reflected over the x-axis

d)

Stretched by a factor of 2

e)

Right 3

1

2

3

4

1)

2)

3)

4)

EXTRA PRACTICE: Graph Characteristics/Transformations Quadratic

Total questions: 133

Worksheet time: 5hrs 36mins

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