Free Printable Solving Quadratic Equations Review

1.

What are the zeros of the graph shown above?

a)

2 and 6

b)

4 and 2

c)

6 and 9

d)

5 and 1

2.

How many zeros does this parabola have?

a)

3

b)

2

c)

0

d)

1

3.

What are the x- intercepts?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

4.

What are the zeros of the graph?

a)

0 and -3

b)

-1 and 3

c)

2 and 4

d)

-3 and 4

5.

.How many zeros does this parabola have?

a)

3

b)

2

c)

0

d)

1

6.

What are the solutions of this graph?

a)

-2 and 3

b)

-1/2 and -6

c)

-2 and -6

d)

3 and -6

7.

How many solutions does this function have?

a)

two

b)

one

c)

all real numbers

d)

no real solutions

8.

How many solutions does this function have?

a)

two

b)

one

c)

all real numbers

d)

no real solutions

9.

What are the solutions to this function?

a)

x={2}

b)

x={2,0}

c)

x={-2}

d)

x={0,-2}

10.

2 A function has a discriminant of 4.

How many x-intercepts does it have?

a)

0

b)

1

c)

2

d)

4

11.

2 A function has a discriminant of 0.

How many x-intercepts does it have?

a)

0

b)

1

c)

2

d)

5

12.

3 What is the discriminant of

-2x² − x − 1 = 0 ?

a)

76

b)

-7

c)

9

d)

none of these

13.

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

a)

76

b)

29

c)

68

d)

none of these

14.

What is the discriminant for 5x² + x − 2 = 0

a)

-39

b)

42

c)

-41

d)

none of these

15.

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

16.

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

a)

0

b)

1

c)

2

d)

5

17.

A function has a discriminant of -3.
______________
How many x-intercepts does it have?

a)

0

b)

1

c)

2

d)

3

18.

Solve for the discriminant of the given equation -2x² -6x=0

a)

-36

b)

36

c)

0

d)

44

19.

Convert x²- 9x + 20 to factored form and solve.

a)

(x-10)(x+2); x = -2, 10

b)

(x+4)(x+5); x = -5, -4

c)

(x-4)(x-5); x = 4, 5

d)

Not factorable

20.

Factor x²+ 6x + 9 and solve for x.

a)

(x+3)(x+3); x = -3

b)

(x+4)(x+5); x=-4, -5

c)

(x-3)(x-3); x=3

d)

Not factorable

21.

Solve by factoring

a)

-4, 2

b)

-2, 4

c)

-16

d)

-4

22.

Solve by Factoring

x² + 4x - 40 = -8

a)

-10 & -4

b)

-4 & 10

c)

-8 & 4

d)

8 & -4

23.

Solve for x:
(x+6)²=49

a)

x=7,12

b)

x=±7

c)

x=1,-13

d)

x=43,-55

24.

Solve.
2(2x - 4)² = 32

a)

x = 4

b)

x = 10

c)

x = -2

d)

x = 0, 4

25.

x² -4 = 77

a)

9

b)

-9

c)

No Real Solutions

d)

9, -9

26.

Solve by taking the square root:
4x² = 100

a)

-10, 10

b)

-25, 25

c)

-5, 5

d)

5

27.

-5x² = -50

a)

± 5

b)

± 10

c)

± √10

d)

-10

28.

2x²= 30

a)

x= √5

b)

x= √30

c)

x= √15

d)

x= ±5

29.

Solve for x.

-7x² + 92 = 8

a)

x = ± 2√3

b)

x = ± 3√2

c)

x = ± 2√21

d)

x = ± 2√7

30.

Solve for x.

2(x + 5)² = 28

a)

x = 5 ± √14

b)

x = -5 ± 2√7

c)

x = -5 ± √14

d)

x = 5 ± 2√7

31.

Create a Perfect Square Trinomial
x²+ 6x + ____

a)

6

b)

-6

c)

9

d)

-9

32.

Create a Perfect Square Trinomial
x²+ 22x + ____

a)

11

b)

- 11

c)

121

d)

-121

33.

Create a Perfect Square Trinomial
x²- 30x + ____

a)

-15

b)

225

c)

30

d)

25

34.

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

35.

When factoring $x^2-10x+25\ =\ 49$ what goes into the blank $\left(x-....\right)^2=49$

a)

5

b)

10

c)

7

d)

25

36.

What did you need to add to both sides to complete the square? $x^2+12x+$ ___ = $20+$ ___

a)

6

b)

36

c)

10

d)

144

37.

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

a)

4

b)

2

c)

8

d)

20

38.

a)

b)

c)

d)

39.

a)

$\frac{9}{2}$

b)

$\frac{3}{2}$

c)

$\left(\frac{3}{2}\right)^2$

d)

$\left(\frac{9}{2}\right)^2$

40.

Complete the square for the equation:

$x^2-10x+7=0$

a)

$\left(x-5\right)^2=18$

b)

$\left(x+5\right)^2=18$

c)

$\left(x-5\right)^2=-7$

d)

$\left(x+5\right)^2=-7$

41.

Complete the square for the equation:

$x^2-24x+23=0$

a)

$\left(x+12\right)^2=121$

b)

$\left(x-12\right)^2=121$

c)

$\left(x+12\right)^2=144$

d)

$\left(x-12\right)^2=144$

42.

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

43.

Solve 2x² + 7x - 15 = 0 using the quadratic formula

a)

-1.5 or 5

b)

No Solution

c)

-5 or 1.5

d)

0.7 or 5

44.

Solve 8x² - 6x + 1 = 0 using the quadratic formula

a)

No Solution

b)

0 or 1

c)

-0.5 or -0.25

d)

0.25 or 0.5

45.

a)

A

b)

B

c)

C

d)

D

46.

Solve using the Quadratic Formula:
(Hint: Set the equation = to 0)

$x^2+4x-40=-8$

a)

$x=-10,\ -4$

b)

$x=-4,\ 10$

c)

$x=-8,\ 4$

d)

$x=-4,\ 8$

47.

$2x^2=8x+3$

2x^2-8x-3=0

x=\frac{8\pm\sqrt{64-4\left(2\right)\left(-3\right)}}{4}

x=\frac{8\pm\sqrt{40}}{4}

x=\frac{8\pm2\sqrt{10}}{4}

x=\frac{4\pm\sqrt{10}}{2}

Suzanne solved the equation using this process.

Did she make a mistake?

If yes, at which line did she make her first mistake?

(There are 5 steps in her process)

a)

Suzanne made no errors.

b)

Step 2

c)

Step 3

d)

Step 4

e)

Step 5

Solving Quadratic Equations Review

Total questions: 47

Worksheet time: 4hrs 4mins

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