Free Printable Quadratic/Discriminant Test 5th

1.

Determine the values of
a, b, and c for
the quadratic equation:
4x² – 8x = 3

a)

a = 4, b = -8, c = 3

b)

a = 4, b =-8, c =-3

c)

a = 4, b = 8, c = 3

d)

a = 4, b = 8, c = -3

2.

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

a)

-4.9 and -0.1

b)

-8.54 and 8.54

c)

-0.45 and 3.55

d)

-6.77 and 1.77

3.

Solve 2x² + 7x - 15 = 0

a)

-1.5 or 5

b)

No Solution

c)

-5 or 1.5

d)

0.7 or 5

4.

Solve using the quadratic formula.
2x² - 9x - 35 = 0

a)

x = 7/2, x = -6

b)

x = -5/2, x =5

c)

x = -3/7, x =6

d)

x = -5/2, x = 7

5.

What is this formula?

a)

This is the speed of light formula.

b)

This is the quadratic formula.

c)

This is the zero product property.

d)

This is scary.

6.

Identify the 'b' value: y = 16x² -8x -24

a)

16

b)

-8

c)

8

d)

-24

7.

Solve 8x² - 6x + 1 = 0

a)

No Solution

b)

0 or 1

c)

-0.5 or -0.25

d)

0.25 or 0.5

8.

Use the quadratic formula to find the solutions for
y = 2x² - 9x + 5

a)

-8.14 and -6.14

b)

4.07 and 3.07

c)

3.85 and 0.65

d)

ZERO solutions

9.

Factor: x² – 5x – 24

a)

(x - 5)(x + 19)

b)

(x - 8)(x + 3)

c)

(x - 3)(x + 8)

d)

(x - 19)(x + 5)

10.

The quadratic equation can be used to solve quadratic equations that cannot be factored.

a)

True

b)

False

11.

What should you do first in solving this equation?
x² + 6x - 13 = 3

a)

Get factored form

b)

Write down: a=1, b=6, c=-13

c)

Make it equal 0 by subtracting 3 on each side

d)

Type it all in a calculator.

12.

The discriminant is

a)

ax² + bx + c

b)

b - 4ac

c)

b² - 4ac

d)

b² + 4ac

13.

Simplify √-4

a)

2i

b)

-2i

c)

2

d)

4i

14.

a)

-5i

b)

5

c)

5i

d)

-5

15.

If the discriminant equals 0, then the quadratic has:

a)

1 Rational Solution

b)

2 Rational Solutions

c)

No solutions

d)

2 Complex Solutions

16.

If the discriminant is positive but NOT a perfect square, then the quadratic has:

a)

1 Rational Solution

b)

2 Irrational Solutions

c)

2 Rational Solutions

d)

2 Complex Solutions

17.

If the discriminant is negative, then the quadratic has:

a)

1 Rational Solution

b)

2 Rational Solutions

c)

2 Irrational Solutions

d)

2 Complex Solutions

18.

Solve x² - 5x + 10 = 0

a)

(5 - i√15)/2 , (5 + i√15)/2

b)

(5 - √15)/2 , (5 + √15)/2

c)

(5 - i√65)/2 , (5 + i√65)/2

d)

(5 - √65)/2 , (5 + √65)/2

19.

Simplify √-121

a)

-11

b)

-121

c)

11i

d)

error

20.

Solve for x:

3x² - 6x + 6 = 0

a)

x = 1± i

b)

x = 3, -6

c)

x = 4.8, 2.7

d)

Undefined

21.

Solve Using the Quadratic Formula
x² + 4x - 40 = -8

a)

-10 & -4

b)

-4 & 10

c)

-8 & 4

d)

8 & -4

22.

a)

A

b)

B

c)

C

d)

D

23.

Use the quadratic formula to solve 2x² + 2x - 12?

a)

-2, 3

b)

2, 3

c)

2, -3

d)

-2, -3

24.

In the equation
y = x² +5x +7, match each leading coefficient with its correct letter

a)

a=0, b=5, c=7

b)

a=1, b=5, c=7

c)

a=7, b=5, c=1

25.

Solve
2x² + 7x - 15 = 0

a)

-1.5 or 5

b)

No Solution

c)

-5 or 1.5

d)

0.7 or 5

26.

Solve using the quadratic formula...
9x² = 4 + 7x

a)

x = 2 and x = 3

b)

x = -1 and x = .25

c)

x = 1 and x = -.45

d)

x = 1.16, and x = -.38

27.

a)

A

b)

B

c)

C

d)

D

28.

How many solutions does the equation 4x² + 4x + 1 = 0 have?

a)

0

b)

1

c)

2

d)

More than 2

29.

find x for
2x²-8x-24=0

a)

x= 6, -2

b)

x= 2, -6

c)

x= 4, 2

d)

x= 2, 6

30.

Use the quadratic formula to find the solutions for
y = -x² - 5x + 12

a)

-4.9 and -0.1

b)

-8.54 and 8.54

c)

-0.45 and 3.55

d)

-6.77 and 1.77

31.

Solve Using the quadratic formula

a)

A

b)

B

c)

C

d)

D

32.

a)

4,1/8

b)

3, -1/5

c)

5,2

d)

3,0

33.

a)

4,-1

b)

8/3,9/5

c)

1/5,3/7

d)

7,-2

34.

a)

4, -5/3

b)

2/3, 6

c)

4/7,6

d)

-3/8,-7

35.

What should you do first in solving this equation?
x² + 6x - 13 = 3

a)

Get factored form

b)

Write down: a=1, b=6, c=-13

c)

Make it equal 0 by subtracting 3 on each side

d)

Type it all in a calculator.

36.

The discriminant is

a)

aX² + bX + c

b)

b - 4ac

c)

b² - 4ac

d)

b² + 4ac

37.

____________
For the function above, is the discriminant positive, negative, or zero?

a)

Positive

b)

Negative

c)

Zero

d)

Not Sure

38.

____________
For the function above, is the discriminant positive, negative, or zero?

a)

Positive

b)

Negative

c)

Zero

d)

Not Sure

39.

For the function below, is the discriminant positive, negative, or zero?

___________

y = x² + 4x + 4

a)

Positive

b)

Negative

c)

Zero

d)

Not Sure

40.

What is the discriminant of -2x² − x − 1 = 0

a)

76

b)

-7

c)

9

d)

none of these

41.

What is the discriminant of 6x² − 2x − 3 = 0

a)

76

b)

29

c)

68

d)

none of these

42.

If the discriminant is positive, then the solution will be

a)

one real solution

b)

two real solutions

c)

no real solutions

d)

one imaginary solution

43.

A function has a discriminant of 25.
______________
How many solutions does it have?

a)

0

b)

1

c)

2

d)

5

44.

In the equation
y = x² +5x +7, match each leading coefficient with its correct letter

a)

a=0, b=5, c=7

b)

a=1, b=5, c=7

c)

a=7, b=5, c=1

45.

Determine the values of

a, b, and c for

the quadratic equation:

4x² – 8x = 3

a)

a = 4, b = -8, c = 3

b)

a = 4, b =-8, c =-3

c)

a = 4, b = 8, c = 3

d)

a = 4, b = 8, c = -3

46.

Determine the value of the discriminant and name the nature of the roots for the following:
x² + 7x + 13
Remember: b² - 4ac

a)

400, 2 real root

b)

0, 1 real root with a multiplicity of 2

c)

-400, 2 imaginary roots

d)

-3, 2 imaginary roots

47.

How many solutions will this quadratic equation x²+8x+16 has?

a)

2 real solutions

b)

2 imaginary solution

c)

1 solution

d)

3 solutions

48.

What is the discriminant and how many solutions would this quadratic have?

x² - 6x + 9 = 0

a)

0, No Solutions

b)

0, 1 Solution

c)

72, 2 Solutions

d)

-72, No Solution

49.

What is the discriminant and how many solutions would this quadratic have?

-8x² + 6x - 4 = 0

a)

-92, 2 Imaginary Solutions

b)

164, 2 Solutions

c)

-164, No Solutions

d)

92, 2 Solutions

50.

What is the discriminant and how many solutions would this quadratic have?

4x² + 6x - 4 = 0

a)

-28, No Solutions

b)

28, 2 Solutions

c)

100, 2 Solutions

d)

-100, No Solutions

51.

What is the discriminant of this equation?

3x² + 8x = 0

a)

64

b)

52

c)

9

d)

0

52.

What is the discriminant and how many solutions would this quadratic have?

-3x² - 5x + 15 = 7

a)

205, 2 Solutions

b)

-71, No Solutions

c)

121, 2 Solutions

d)

121, 1 Solution

53.

What is the discriminant and how many solutions would this quadratic have?

3x² + 3x + 4 = -3

a)

-75, No Solutions

b)

-75, 2 Solutions

c)

-39, No Solutions

d)

-39, 1 Solution

54.

Solve for x:

3x² - 6x + 6 = 0

a)

x = 1± i

b)

x = 3, -6

c)

x = 4.8, 2.7

d)

Undefined

55.

Solve x² - 5x + 10 = 0

a)

(5 - i√15)/2 , (5 + i√15)/2

b)

(5 - √15)/2 , (5 + √15)/2

c)

(5 - i√65)/2 , (5 + i√65)/2

d)

(5 - √65)/2 , (5 + √65)/2

56.

The discriminant is

a)

aX² + bX + c

b)

b - 4ac

c)

b² - 4ac

d)

b² + 4ac

57.

What does the discriminant tell us?

a)

The maximum or minimum

b)

The y-intercept

c)

The number and type of solutions

d)

The axis of symmetry

58.

A function has a discriminant of 0.

How many x-intercepts does it have?

a)

0

b)

1

c)

2

d)

5

59.

Use the discriminant to determine the number of solutions 4x² + 4x + 1 = 0 has?

a)

0

b)

1

c)

2

d)

More than 2

60.

Use the quadratic formula to solve 2x² + 2x - 12?

a)

-2, 3

b)

2, 3

c)

2, -3

d)

-2, -3

61.

If the discriminant is negative, you will have....

a)

two real solutions

b)

two irrational solutions

c)

two complex numbers

d)

one solution

62.

Use the discriminant to determine the number of solutions the following quadratic equation has.

-2x² − x − 1 = 0

a)

76 Two Solutions

b)

-7 No Solutions

c)

9 Two Solutions

d)

0 One Solution

63.

Use the discriminant to determine the number of solutions the following quadratic equation has.

6x² − 2x − 3 = 0

a)

76 Two Solutions

b)

29 Two Solutions

c)

68 Two Solutions

d)

none of these

64.

What is the discriminant and how many solutions would this quadratic have?

4x² + 6x - 4 = 0

a)

-28, No Solutions

b)

28, 2 Solutions

c)

100, 2 Solutions

d)

-100, No Solutions

65.

Solve using the quadratic formula.
2x² - 9x - 35 = 0

a)

x = 7/2, x = -6

b)

x = -5/2, x =5

c)

x = -3/7, x =6

d)

x = -5/2, x = 7

66.

2x²-x -3=0

a)

x=-3/2 x=1

b)

x= 3/2 x= -1

c)

x= -3/2 x= -1

d)

x= 3/2 x= 1

67.

Solve 2x² + 7x - 15 = 0

a)

-1.5 or 5

b)

No Solution

c)

-5 or 1.5

d)

0.7 or 5

68.

$w^2+7w+4=0$

a)

$\frac{-7\pm\sqrt{33}}{2}$

b)

$\frac{-7\pm\sqrt{65}}{2}$

c)

$\frac{7\pm\sqrt{33}}{2}$

d)

$\frac{-7\pm3\sqrt{11}}{2}$

69.

The discriminant is

a)

ax² + bx + c

b)

b - 4ac

c)

b² - 4ac

d)

b² + 4ac

70.

If the discriminant equals 0, then the quadratic has:

a)

1 Rational Solution

b)

2 Rational Solutions

c)

No solutions

d)

2 Complex Solutions

71.

If the discriminant is negative, you will have....

a)

two real solutions

b)

two irrational solutions

c)

No solutions

d)

one solution

72.

1 What does the discriminant tell us?

a)

The maximum or minimum

b)

The y-intercept

c)

The number and type of solutions

d)

The axis of symmetry

73.

3 What is the discriminant of

-2x² − x − 1 = 0 ?

a)

76

b)

-7

c)

9

d)

none of these

74.

3 For the function above, is the discriminant positive, negative, or zero?

a)

Positive

b)

Negative

c)

Zero

75.

3 For the function above, is the discriminant positive, negative, or zero?

a)

Positive

b)

Negative

c)

Zero

76.

What is the discriminant and how many solutions would this quadratic have?

-8x² + 6x - 4 = 0

a)

-92, No Solutions

b)

164, 2 Solutions

c)

-164, No Solutions

d)

92, 2 Solutions

77.

What is the discriminant and how many solutions would this quadratic have?

4x² + 6x - 4 = 0

a)

-28, No Solutions

b)

28, 2 Solutions

c)

100, 2 Solutions

d)

-100, No Solutions

78.

What is the discriminant of this equation?

-5x² - 6 = 0

a)

120

b)

36

c)

16

d)

-120

79.

What is the discriminant and how many solutions would this quadratic have?

-3x² - 5x + 15 = 7

a)

205, 2 Solutions

b)

-71, No Solutions

c)

121, 2 Solutions

d)

121, 1 Solution

80.

What is the discriminant and how many solutions would this quadratic have?

-4x² - 8x - 8 = -4

a)

0, No Solutions

b)

0, 1 Solution

c)

128, 2 Solutions

d)

128, 1 Solution

81.

To solve by completing the square, what needs to be moved in this equation?
x² = 9 - 4x

a)

the -4x

b)

the 9

c)

the x²

82.

What is the first step to solving THIS equation by completing the square?
a² + 10a + 21 = 0

a)

Set the equation equal to zero

b)

Divide 10 by 2 and add the result to both sides

c)

Add a² and 10a together

d)

Subtract the 21

83.

When do you use the plus or minus symbol?
±

a)

After taking the square root of both sides

b)

After adding the square to both sides

c)

After taking half of b

d)

After setting the equation equal to zero

84.

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

a)

No Real Solution

b)

c)

d)

85.

What is one of the solutions to this equation?
(2x - 1)² = 49

a)

7

b)

-7

c)

-4

d)

-3

86.

Solve by completing the square.
x² +12x = 5

a)

X = 6 + √41 or 6 − √41

b)

X= 35 or 47

c)

X = −6 + √41 or −6 − √41

d)

X = √35 or √47

87.

Which equation shows $x^2+8x+9=0$ after the method of completing the square has been applied?

a)

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

b)

$\left(x+4\right)^2=7$

c)

$\left(x+8\right)^2=55$

d)

$x^2=-\left(8x+9\right)$

88.

When $2x^2-20x+49=19$ is written in the form $\left(x-p\right)^2=q$ , what is the value of $q$ ?

a)

19

b)

10

c)

5

d)

-30

89.

Solve $36x^2+169\ =\ 0$ .

a)

$x=\pm\frac{6}{13}i$

b)

$x=\pm\frac{6}{13}$

c)

$x=\pm\frac{13}{6}i$

d)

$x=\pm\frac{13}{6}$

90.

Solve $x^2-4x+18=0$ .

a)

$x=-2\pm i\sqrt{14}$

b)

$x=-2\pm\sqrt{14}$

c)

$x=2\pm i\sqrt{14}$

d)

$x=2\pm\sqrt{14}$

91.

Solve $4x^2+5x+2=0$ .

a)

$x=\frac{5}{8}\pm\frac{\sqrt{7}}{8}$

b)

$x=-\frac{5}{8}\pm\frac{\sqrt{7}}{8}i$

c)

$x=-\frac{5}{8}\pm\frac{\sqrt{7}}{8}$

d)

$x=\frac{5}{8}\pm\frac{\sqrt{7}}{8}i$

92.

Solve $x^2+10x=39$ .

a)

$x=-5\pm\sqrt{14}$

b)

$x=-3\ or\ 13$

c)

$x\ =\ 3\ or\ -13$

d)

$x=5\pm\sqrt{14}$

93.

What do you do to the b value to correctly complete the square?

a)

square it

b)

divide it by 2 and square the result

c)

divide it by 2 and take the square root of the result

d)

divide it by 2 only

94.

Complete the square for
x² + 12x + ____

a)

x² + 12x + 144

b)

x² + 12x + 36

c)

x² + 12x - 36

d)

x² + +12x - 144

95.

Solve Using the Quadratic Formula
2x² + 7x - 15 = 0

a)

-1.5 or 5

b)

No Solution

c)

-5 or 1.5

d)

0.7 or 5

96.

Out of all of the methods we have learned for solving quadratic functions, which method is your favorite?

a)

Factoring

b)

Completing the Square

c)

Quadratic Formula

d)

Graphing

97.

$2x^2+3x-4=0$ When the quadratic formula is applied to , what is the numerator of the simplified answer?

a)

$3\pm\sqrt{41}$

b)

$-3\pm\sqrt{41}$

c)

$3\pm\sqrt{38}$

d)

$-3\pm\sqrt{-23}$

98.

How could you determine how many solutions that a Quad. Equation has?

a)

Solve to find the solutions

b)

Using discriminant

c)

Using a, b, c: the coefficients of the Quad. Equation

d)

You can't tell

99.

When factoring
x² - 4x + 4 = 20,
what goes in the blank?
(x - __ )² = 20

a)

4

b)

2

c)

8

d)

20

100.

The discriminant is

a)

aX² + bX + c

b)

b - 4ac

c)

b² - 4ac

d)

b² + 4ac

101.

Use the quadratic formula to solve 2x² + 2x - 12?

a)

-2, 3

b)

2, 3

c)

2, -3

d)

-2, -3

102.

.How many roots does this parabola have?

a)

3

b)

2

c)

0

d)

1

103.

If the discriminant is positive, then the solution will be

a)

one real solution

b)

two real solutions

c)

no real solutions

d)

one imaginary solution

104.

What does the discriminant tell us?

a)

The maximum or minimum

b)

The y-intercept

c)

The number and type of solutions

d)

The axis of symmetry

105.

Which graph has a discriminant = 0?

a)

None of them

b)

Red

c)

Blue

d)

Green

106.

Use the discriminant to determine the number of solutions 4x² + 4x + 1 = 0 has?

a)

0

b)

1

c)

2

d)

More than 2

107.

Solve Using the Quadratic Formula
x² + 4x - 40 = -8

a)

-10 & -4

b)

-4 & 10

c)

-8 & 4

d)

8 & -4

108.

Use the quadratic formula to find the solutions for
y = -x² - 5x + 12

a)

-4.9 and -0.1

b)

-8.54 and 8.54

c)

-0.45 and 3.55

d)

-6.77 and 1.77

109.

What is the formula for the discriminant?

a)

$b^2-4ac$

b)

$b^2+4ac$

c)

$c^2-4ab$

d)

$a^2-4bc$

110.

When the discriminant is positive, there are ________ solutions

a)

2 Real

b)

1 Real

c)

2 Imaginary

d)

None

111.

When the discriminant is negative, there are ________ solutions.

a)

2 Real

b)

1 Real

c)

2 Imaginary

d)

None

112.

Given, a= 3, b= 4 and c= 1, what does the discriminant look like?

a)

$\left(3\right)^2-4\left(4\right)\left(1\right)$

b)

$\left(1\right)^2-4\left(4\right)\left(3\right)$

c)

$\left(4\right)^2-4\left(3\right)\left(1\right)$

113.

Given, a= 2, b= -5 and c= 6, what does the discriminant look like?

a)

$\left(-5\right)^2-4\left(2\right)\left(6\right)$

b)

$\left(6\right)^2-4\left(2\right)\left(-5\right)$

c)

$\left(2\right)^2-4\left(-5\right)\left(6\right)$

114.

Given the discriminant is -92, how many solutions are there?

a)

2 Real

b)

1 Real

c)

2 Imaginary

d)

None

115.

Given the discriminant is 0, how many solutions are there?

a)

2 Real

b)

1 Real

c)

2 Imaginary

d)

None

Quadratic/Discriminant Test 5th

Total questions: 115

Worksheet time: 6hrs 17mins

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