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Worksheets

OLD U5 - Quadratic Functions

Total questions: 143

Worksheet time: 1hrs 13mins

Name
Class
Date
1.

What is the equation for the axis of symmetry of the parabola? Do not type spaces.

(a)  

2.

Use the "axis of symmetry formula" to find the vertex of the parabola.  Write your answer as an ordered pair (x,y)

y=3x2−12x+5y=3x^2-12x+5  



(a)  

3.

What is the equation for the axis of symmetry of the parabola? Do not type spaces.

y=3x2−12x+5y=3x^2-12x+5  



(a)  

4.

What is the vertex for the parabola? Write your answer as an ordered pair (x,y). Do not type spaces.

(a)  

5.

What is the equation for the axis of symmetry for the pictured parabola? Do not type spaces.

(a)  

6.

What is the vertex for the pictured parabola? Write as an ordered pair (x,y). Do not type spaces.

(a)  

7.

What is the equation for the axis of symmetry for the given quadratic? Do not type spaces.

y=2x2−8x+9y=2x^2-8x+9  

(a)  

8.

SAT Question: Find the vertex of the given quadratic function. What is the product of the x and y value? Do not type spaces.

y=2x2−8x+19y=2x^2-8x+19  

(a)  

9.

What is the equation for the axis of symmetry for the given parabola? Do not type spaces.

(a)  

10.

What is the vertex for the given parabola? Write as an ordered pair (x,y). Do not type spaces.

(a)  

11.

SAT Question: Find the vertex of the quadratic function. Then find the sum of the x and y value. Do not type spaces.

y=6x2−12x+7y=6x^2-12x+7  

(a)  

12.

What is the vertex of the following quadratic function? Write your answer as an ordered pair (x,y). Do not type spaces.

y=6x2−12y=6x^2-12  

(a)  

13.

What is the vertex of the following quadratic function? Write your answer as an ordered pair (x,y). Do not type spaces.

y=6x2−12xy=6x^2-12x  

(a)  

14.

What is the vertex of the given quadratic function? Write your answer as an ordered pair (x,y). Do not type spaces.

y=x2−8x+4y=x^2-8x+4  

(a)  

15.

What is the vertex of the given quadratic function? Write your answer as an ordered pair (x,y). Do not type spaces.

y=x2+4xy=x^2+4x  

(a)  

16.

What is the vertex of the given quadratic function? Write your answer as an ordered pair (x,y). Do not type spaces.

y=x2+4y=x^2+4  

(a)  

17.

What is the equation of the axis of symmetry for the given quadratic function? Do not type spaces.

y=x2−8x+4y=x^2-8x+4  

(a)  

18.

What is the equation of the axis of symmetry for the given quadratic function? Do not type spaces.

y=x2+4y=x^2+4  

(a)  

19.

What is the equation of the axis of symmetry for the given quadratic function? Do not type spaces.

y=x2+4xy=x^2+4x  

(a)  

20.

What is the equation of the axis of symmetry for the given quadratic function? Do not type spaces.

y=6x2−12xy=6x^2-12x  

(a)  

21.

What is the vertex of the given quadratic function? Write as an ordered pair (x,y). Do not type spaces.

(a)  

22.

What is the equation of the axis of symmetry for the given quadratic function? Do not type spaces.

(a)  

23.

What is the vertex of the given quadratic function? Write as an ordered pair (x,y). Do not type spaces.

(a)  

24.

What is the equation of the axis of symmetry for the given quadratic function? Do not type spaces.

(a)  

25.

What is the table for the following equation with the vertex in the middle?

y=4x2−16x+7y=4x^2-16x+7  

a)
b)
c)
d)
26.

What is the equation for the axis of symmetry of the given parabola? Do not type spaces.

(a)  

27.

What is the vertex of the given parabola?  Do not type spaces.

(a)  

28.

Use the "axis of symmetry formula" to find the vertex of the equation. Write as an ordered pair (x,y).  y=2x2+8x+3y=2x^2+8x+3  



(a)  

29.

What is the equation for the axis of symmetry for the following quadratic function? Do not type spaces.

y=2x2+8x+3y=2x^2+8x+3  



(a)  

30.

What is the vertex of the following quadratic function? Write as an ordered pair (x,y). Do not type spaces.

y=−2x2−12xy=-2x^2-12x  

(a)  

31.

What is the equation for the axis of symmetry of the following quadratic function? Do not type spaces.

y=−2x2−12xy=-2x^2-12x  

(a)  

32.

What is the vertex of the given function? Do not type spaces.

y=−2x2−12y=-2x^2-12  

(a)  

33.

What is the equation for the axis of symmetry? Do not type spaces.

y=−2x2−12y=-2x^2-12  

(a)  

34.

y=3x2−6x+2y=3x^2-6x+2  

Which table is for the graph of the equation and has the vertex in the middle?

a)
b)
c)
d)
35.

y=(x+3)(x+1)y=\left(x+3\right)\left(x+1\right)  
Which table is for the graph of the equation and has the vertex in the middle?

a)
b)
c)
d)
36.

Match the following

a)
1.

Quadratic Function

b)
2.

Linear Function

c)
3.

Exponential Function

d)
4.

Not a function

37.

Match the following

a)
1.

Not a function

b)
2.

Quadratic Function

c)
3.

Exponential Function

d)
4.

Linear Function

38.

Match the following

a)

y=−2x+1y=-2x+1

1.

Linear Function

b)

y=−2x2+7x+1y=-2x^2+7x+1

2.

Quadratic Function

c)

y=−2xy=-2^x

3.

Exponential Function

d)

x=−2x=-2

4.

Not a function

39.

Match the following

a)

y=4x−2y=4x-2

1.

Linear Function

b)

y=4x2−2x+7y=4x^2-2x+7

2.

Quadratic Function

c)

y=−4xy=-4^x

3.

Exponential Function

d)

x=−4x=-4

4.

Not a function

40.

Which are quadratic functions? Select all that apply.

a)

b)

c)

y=−3x2+7x−9y=-3x^2+7x-9

d)

y=−3xy=-3^x

e)

41.

Which are quadratic functions? Select all that apply.

a)

b)

c)

d)

y=x2y=x^2

e)

y=2xy=2^x

42.

What is the equation for the axis of symmetry of the parabola?

a)

x=−2x=-2

b)

−2-2

c)

(−2,1)\left(-2,1\right)

d)

y=1y=1

43.

Use the "axis of symmetry formula" to find the vertex of the equation. Write as an ordered pair.

y=2x2+8x−9y=2x^2+8x-9  



(a)  

44.

Which graph is a quadratic function that has a range of R:{y<=-2}?

a)
b)
c)
d)
e)

45.

What is the range of the following quadratic function? Use correct notation. Do not type spaces.

y=−3x2−6x−13y=-3x^2-6x-13  

(a)  

46.

What is the equation for the axis of symmetry of the following quadratic function? Do not type spaces.

y=−3x2−6x−13y=-3x^2-6x-13  

(a)  

47.

What is the range for the given quadratic function? Use correct notation. Do not type spaces.

y=−x2−8x+1y=-x^2-8x+1  

(a)  

48.

What is the vertex for the given quadratic function? Do not type spaces.

y=−x2−8x+1y=-x^2-8x+1  

(a)  

49.

What is the range of the quadratic function? Use correct notation. Do not type spaces.

(a)  

50.

What is the vertex of the quadratic function? Do not type spaces.

(a)  

51.

What is the range of the quadratic function? Use correct notation. Do not type spaces.

(a)  

52.

What is the equation for the axis of symmetry of the quadratic function? Do not type spaces.

(a)  

53.

What is the range for the given quadratic function? Use correct notation. Do not type spaces.

y=4x2−8x+7y=4x^2-8x+7  

(a)  

54.

What is the equations for the axis of symmetry for the given quadratic function? Do not type spaces.

y=4x2−8x+7y=4x^2-8x+7  

(a)  

55.

Select all points that are solutions to the quadratic function.

0=x2−4x−120=x^2-4x-12  

a)

(−2,0)\left(-2,0\right)  

b)

(6,0)\left(6,0\right)  

c)

(2,−16)\left(2,-16\right)  

d)

R:{y≥−16}R:\left\{y\ge-16\right\}   

e)

no solution 

56.

Use the "axis of symmetry formula" to find the vertex. Write your answer as an ordered pair (x,y) y=3x2−6x+7y=3x^2-6x+7  



(a)  

57.

How many solutions are there to the quadratic function?

0=x2−4x−120=x^2-4x-12  

a)

 2 solutions

b)

 1 solution

c)

 no solutions

58.

Select all points that are solutions to the quadratic equation.

0=x2+6x+90=x^2+6x+9  

a)

(-3,0)

b)

(0,-3)

c)

(3,0)

d)

no solution

59.

What is the vertex of the given parabola? Do not type spaces.

 

(a)  

60.

Select all points that are solutions to the given quadratic function.

x2−4x+5=0x^2-4x+5=0  

a)

no solution

b)

(2,1)

c)

x=2

d)

(0,5)

e)

(1,2)

61.

What is the vertex of the given parabola?

 

a)

no solution

b)

(2,1)

c)

x=2

d)

(0,5)

e)

(1,2)

62.

What is the equation for the axis of symmetry of the given parabola?

 

a)

no solution

b)

(2,1)

c)

x=2

d)

(0,5)

e)

(1,2)

63.

Select all points that are solutions to the given parabola.

x2−4x−5=0x^2-4x-5=0  

a)

(-1,0)

b)

(5,0)

c)

no solution

d)

(2,-9)

e)

x=2

64.

What is the vertex of the given parabola?

a)

(-1,0)

b)

(5,0)

c)

no solution

d)

(2,-9)

e)

x=2

65.

What is the equation for the axis of symmetry of the given parabola?

a)

(-1,0)

b)

(5,0)

c)

no solution

d)

(2,-9)

e)

x=2

66.

Select all quadratic functions that have 2 solutions.

a)
b)
c)
d)
e)
67.

Select all quadratic functions that have 1 solution.

a)
b)
c)
d)
e)
68.

What is the range of the given parabola? Use correct notation. Do not type spaces.

(a)  

69.

What is the range of the given parabola? Use correct notation. Do not type spaces.

(a)  

70.

Select all quadratic functions that have no solutions.

a)
b)
c)
d)
e)
71.

Select all that have a negative "a" value

a)

y=∣x−2∣+3y=\left|x-2\right|+3  

b)

y=−∣x+2∣+3y=-\left|x+2\right|+3  

c)
d)
e)

y=23∣x∣y=\frac{2}{3}\left|x\right|  

72.

Select all that have a vertex of (2,3)

a)

y=∣x−2∣+3y=\left|x-2\right|+3  

b)

y=−∣x+2∣+3y=-\left|x+2\right|+3  

c)
d)
e)

y=23∣x∣y=\frac{2}{3}\left|x\right|  

73.

Select all that have a vertex of (0,3)

a)

y=∣x−1∣+3y=\left|x-1\right|+3

y=∣x−1∣+3

b)

y=​14∣x∣+3y=\frac{​1}{4}∣x∣+3

y=4


​1

​∣x∣+3

c)

y=∣x+3∣y=\left|x+3\right|

y=∣x+3∣

d)
e)
74.

Select all that have positive "a" value.

a)

y=∣x−3∣y=\left|x-3\right|  

b)

y=14∣x∣+3y=\frac{1}{4}\left|x\right|+3  

c)

y=−25∣x+3∣y=\frac{-2}{5}\left|x+3\right|  

d)
e)
75.

Which graph matches the equation?

y=14∣x−1∣y=\frac{1}{4}\left|x-1\right|  

a)
b)
c)
d)
76.

Which graph matches the equation?

y=14∣x−1∣y=\frac{1}{4}\left|x-1\right|  

a)
b)
c)
d)
77.

Which graph matches the equation?

y=−14∣x−1∣y=\frac{-1}{4}\left|x-1\right|  

a)
b)
c)
d)
78.

What is the vertex of the absolute value function? Write as an ordered pair (x,y).

y=23∣x−1∣+5y=\frac{2}{3}\left|x-1\right|+5  

(a)  

79.

What is the vertex of the absolute value function? Write as an ordered pair (x,y).

y=23∣x+1∣+5y=\frac{2}{3}\left|x+1\right|+5  

(a)  

80.

What is the vertex of the absolute value function? Write as an ordered pair (x,y).

y=−4∣x−2∣−3y=-4\left|x-2\right|-3  

(a)  

81.

What is the vertex of the absolute value function? Write as an ordered pair (x,y).

y=−4∣x+2∣−3y=-4\left|x+2\right|-3  

(a)  

82.

What is the equation for the axis of symmetry?

83.

What is the vertex for the given quadratic function?

(a)  

84.

How many solutions does the given quadratic function have?

a)

Two solutions

b)

One solution

c)

No solutions

85.

What is the equation for the axis of symmetry for the given quadratic function?

f(x)=−2x2−12x+5f\left(x\right)=-2x^2-12x+5

86.

What is the vertex for the given quadratic function?

f(x)=−2x2−12x+5f\left(x\right)=-2x^2-12x+5

(a)  

87.

Match the following

a)
1.

Quadratic function with a positive a coefficient

b)
2.

Quadratic function with a negative a coefficient

c)
3.

Absolute Value function with a positive a coefficient

d)
4.

Absolute Value function with a negative a coefficient

e)
5.

Not a function

88.

Match the following

a)

x=1x=1

1.

Not a function

b)

y=x2−3x−9y=x^2-3x-9

2.

Quadratic function with a positive a coefficient

c)

y=−2x2+4x+8y=-2x^2+4x+8

3.

Quadratic function with a negative a coefficient

d)

y=∣x−1∣−2y=\left|x-1\right|-2

4.

Absolute value function with a positive a coefficient

e)

y=−3∣x+4∣+1y=-3\left|x+4\right|+1

5.

Absolute value function with a negative a coefficient

89.

Which of the following are quadratic functions with a vertex of (-1,2)? Select all that apply.

a)

y=−3(x−1)2+2y=-3\left(x-1\right)^2+2

b)

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

c)

y=−5(x−2)2−1y=-5\left(x-2\right)^2-1

d)

e)

90.

Convert to standard form.

y=−4(x−3)2+5y=-4\left(x-3\right)^2+5

91.

Convert to standard form

y=3(x+6)2−2y=3\left(x+6\right)^2-2

92.

Convert to standard form

y=2(x+5)2−3y=2\left(x+5\right)^2-3

93.

Convert to standard form.

y=−5(x+7)2−1y=-5\left(x+7\right)^2-1

94.

Match the following equations to the correct vertex

a)

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

1.

(1,3)

b)

g(x)=−2(x+1)2+3g\left(x\right)=-2\left(x+1\right)^2+3

2.

(-1,3)

c)

h(x)=−2(x−1)2−3h\left(x\right)=-2\left(x-1\right)^2-3

3.

(1,-3)

d)

j(x)=−2(x+1)2−3j\left(x\right)=-2\left(x+1\right)^2-3

4.

(-1,-3)

95.

What is the range of the given function?

y=−4(x−3)2+5y=-4\left(x-3\right)^2+5

(a)  

96.

What is the range of the given function?

y=3(x+6)2−2y=3\left(x+6\right)^2-2

(a)  

97.

Match the following quadratic functions to the correct range.

a)

y=(x−2)2+3y=\left(x-2\right)^2+3

1.

R:{y>=3}

b)

y=6(x−2)2−3y=6\left(x-2\right)^2-3

2.

R:{y>=-3}

c)

y=−5(x+2)2+3y=-5\left(x+2\right)^2+3

3.

R:{y<=3}

d)

y=−4(x+2)2−3y=-4\left(x+2\right)^2-3

4.

R:{y<=-3}

98.

Which graph represents the given equation?

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

a)

b)

c)

d)

99.

Which equation represents the given graph?

a)

y=−(x+2)2y=-\left(x+2\right)^2

b)

y=(x+2)2y=\left(x+2\right)^2

c)

y=−(x−2)2y=-\left(x-2\right)^2

d)

y=(x−2)2y=\left(x-2\right)^2

100.

Which of the following have a range of

R:{y≤−1}R:\left\{y\le-1\right\}

a)

f(x)=−2(x−1)2f\left(x\right)=-2\left(x-1\right)^2

b)

g(x)=−3(x+5)2−1g\left(x\right)=-3\left(x+5\right)^2-1

c)

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

d)

e)

101.

Solve by factoring. Select all points that are solutions.

x2+8x+12=0x^2+8x+12=0  

a)

(-6,0)

b)

(-2,0)

c)

(6,0)

d)

(2,0)

e)

no solution

102.

What is the range of the following parabola?  

a)

(2,0)

b)

R:{y≥−1}R:\left\{y\ge-1\right\}

c)

(3, -1)

d)

no solutions

e)

(4,0)

103.

What is the vertex of the following parabola? Do not type spaces.

(a)  

104.

Solve by factoring. Select all points that apply.

x2+13x+12=0x^2+13x+12=0  

a)

(-1,0)

b)

(-12,0)

c)

(-13,0)

d)

(-11,0)

e)

(-3,0)

105.

Solve by factoring. Enter your answer as an ordered pair. If there are two solutions, type in only one. Do not type spaces.

x2−7x+12=0x^2-7x+12=0  

(a)  

106.

Solve by factoring. Enter your answer as an ordered pair. If there are two solutions, type in only one. Do not type spaces.

0=x2−3x−100=x^2-3x-10  

(a)  

107.

Solve by factoring. Enter your answer as an ordered pair. If there are two solutions, type in only one. Do not type spaces.

x2−3x=0x^2-3x=0  

(a)  

108.

Solve by factoring. Enter your answer as an ordered pair. If there are two solutions, type in only one. Do not type spaces.

0=x2+8x+160=x^2+8x+16  

(a)  

109.

Solve by factoring. Enter your answer as an ordered pair. If there are two solutions, type in only one. Do not type spaces.

x2+10x+16=0x^2+10x+16=0  

(a)  

110.

Solve by factoring. Enter your answer as an ordered pair. If there are two solutions, type in only one. Do not type spaces.

0=x2+6x+90=x^2+6x+9  

(a)  

111.

Solve by factoring. Enter your answer as an ordered pair. If there are two solutions, type in only one. Do not type spaces.

x2−6x+9=0x^2-6x+9=0  

(a)  

112.

Solve by factoring. Enter your answer as an ordered pair. If there are two solutions, type in only one. Do not type spaces.

0=x2−10x+90=x^2-10x+9  

(a)  

113.

Find the vertex of the given quadratic function. Write your answer as an ordered pair. Do not type spaces.

y=x2−8x+12y=x^2-8x+12  

(a)  

114.

Match the following

a)
1.

Quadratic Function with 2 Solutions

b)
2.

Not a function

c)
3.

Absolute Value function

d)
4.

Quadratic Function with 1 solution

e)
5.

Quadratic Function with no solutions

115.

Which of the following are true for the following parabola? Select all that apply.

a)

The discriminant is a positive number

b)

The discriminant is a negative number

c)

The discriminant is zero

d)

"a" coefficient is positive

e)

"a" coefficient is negative

116.

What is the vertex of the following parabola? Write as an ordered pair.

(a)  

117.

What is the range of the parabola? Use correct notation.

(a)  

118.

Use the "axis of symmetry" formula to find the vertex. y=−2x2+8x−10y=-2x^2+8x-10  



(a)  

119.

What is the discriminant of the following quadratic function?

y=3x2−5x+10y=3x^2-5x+10  

(a)  

120.

Use the discriminant to find the number of solutions of the following quadratic function.

y=x2−5x+2y=x^2-5x+2  

a)

2 solutions

b)

1 solution

c)

no solutions

121.

What is the discriminant of the quadratic function?

y=x2−3xy=x^2-3x  

(a)  

122.

Use the discriminant to find the number of solutions of the quadratic function.

y=x2−3x−2y=x^2-3x-2  

a)

2 solutions

b)

1 solution

c)

no solutions

123.

Which of the following are quadratic functions that have a negative discriminant? Select all that apply.

a)
b)
c)
d)
e)
124.

Which of the following quadratic functions have a positive discriminant? Select all that apply.

a)
b)
c)
d)
e)
125.

What is the discriminant of the quadratic function?

y=7x2+8x−3y=7x^2+8x-3  

(a)  

126.

What is the discriminant of the following quadratic function?

y=x2−16y=x^2-16  

(a)  

127.

Which of the following quadratic functions have a discriminant value of zero? Select all that apply.

a)
b)
c)
d)
e)
128.

Match the following

a)
1.

Discriminant is 0

"a" coefficient is positive

b)
2.

Discriminant is positive

"a" coefficient is negative

c)
3.

Discriminant is positive

"a" coefficient is positive

d)
4.

Not a function

e)
5.

Discriminant is negative.

"a" coefficient is positive.

129.

Solve by using the quadratic formula. There are two solutions. Only give one of them. Write as an ordered pair. Round to the nearest hundredth.

0=6x2+10x+10=6x^2+10x+1  

(a)  

130.

Solve using the quadratic formula. There are two solutions. Only give one of them. Write as an ordered pair. Round to the nearest hundredth.

7x2+13x+2=07x^2+13x+2=0  

(a)  

131.

What is the discriminant of the quadratic function?

0=6x2+10x+10=6x^2+10x+1  

(a)  

132.

What is the discriminant of the quadratic function?

7x2+13x+2=07x^2+13x+2=0  

(a)  

133.

What is the vertex of the given parabola?

(a)  

134.

Match the following

a)
1.

Not a function

b)
2.

Absolute Value function

c)
3.

Quadratic function with a positive discriminant

d)
4.

Quadratic function and the discriminant is zero

e)
5.

Exponential function

135.

Solve by using the quadratic formula. Round to the nearest hundredth. If there are two solutions, only type one. Type your answer as an ordered pair. Indicate "no solution" if applicable.

6x2−11x+17=06x^2-11x+17=0  

(a)  

136.

Solve by using the quadratic formula. Round to the nearest hundredth. If there are two solutions, only type one. Type your answer as an ordered pair. Indicate "no solution" if applicable.

−4x2−9x−11=0-4x^2-9x-11=0  

(a)  

137.

Solve by using the quadratic formula. Round to the nearest hundredth. If there are two solutions, only type one. Type your answer as an ordered pair. Indicate "no solution" if applicable.

0=5x2−7x0=5x^2-7x  

(a)  

138.

Solve by using the quadratic formula. Round to the nearest hundredth. If there are two solutions, only type one. Type your answer as an ordered pair. Indicate "no solution" if applicable.

0=−3x2+80=-3x^2+8  

(a)  

139.

If b is not zero, solve by completing the square. If b=0, use "finding the roots". Round to the hundredth. Write only one answer. Write as an ordered pair. Do not type spaces.

x2−10x=38x^2-10x=38  

(a)  

140.

If b is not zero, solve by completing the square. If b=0, use "finding the roots". Round to the hundredth. Write only one answer. Write as an ordered pair. Do not type spaces.

x2=38x^2=38  

(a)  

141.

If b is not zero, solve by completing the square. If b=0, use "finding the roots". Round to the hundredth. Write only one answer. Write as an ordered pair. Do not type spaces.

x2+16x=56x^2+16x=56  

(a)  

142.

If b is not zero, solve by completing the square. If b=0, use "finding the roots". Round to the hundredth. Write only one answer. Write as an ordered pair. Do not type spaces.

x2=56x^2=56  

(a)  

143.

Which parabolas have a negative discriminant? Select all that apply.

a)
b)
c)
d)
e)

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