Wayground
Quadratic equation and functions - Printable Mathematics Worksheets - Wayground

Quadratic equation and functions

43 questions

8th - 8th Grade

Mathematics

Quadratic equation and functions is a free printable Grade 8 mathematics worksheet with 43 multiple-choice questions and a complete answer key. It helps students identify the coefficients a, b, and c after rewriting an equation in standard form, recognize and apply the quadratic formula, and determine solutions to quadratic equations, including equations with the variable on both sides. The worksheet also practises counting the number of solutions, completing the square by finding the needed constant, and recognizing perfect square trinomials as squared binomials. Students work through concise selection-based questions such as identifying the quadratic formula, solving equations with integer solutions, and selecting the correct missing value in expressions like x² + 12x + ____. It is designed for Grade 8 math review, independent practice, or a quick formative assessment, and the answer key supports efficient checking.

Worksheet settings

Font size

S
M
L
XL
Worksheets

Quadratic equation and functions

Total questions: 43

Name
Class
Date
1.

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

(Don't forget it needs to be equal to zero)

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.
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.
3.
Use the quadratic formula to solve 2x2 + 2x - 12?
a)
-2, 3
b)
2, 3
c)
2, -3
d)
-2, -3
4.
Solve Using the Quadratic Formula
 x2 + 4x - 40 = -8
a)
-10 & -4
b)
-4 & 10
c)
-8 & 4
d)
8 & -4
5.
Solve    
2x2 + 7x - 15 = 0
a)
-1.5 or 5
b)
No Solution
c)
-5 or 1.5
d)
0.7 or 5
6.
How many solutions does the equation 4x2 + 4x + 1 = 0 have?
a)
0
b)
1
c)
2
d)
More than 2
7.

Solve using the Quadratic Formula


4x2 - 7x = -3

a)

x = 1, 0.75

b)

x = -1, -0.75

c)

x = 2.11, -0.36

d)

x = -2.11, 0.36

8.
9x+3=21 what does x equal?
a)
x=3
b)
x=2
c)
x=4
d)
x=8
9.

Solve using the quadratic formula.

2n2-2n-12=0

a)

8, 2

b)

2, -3

c)

3, -2

d)

2, -12

10.
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
11.

Complete the square for

x2 + 12x + ____

(find the missing number in the blank)

a)

x2 + 12x + 144

b)

x2 + 12x + 36

c)

x2 + 12x - 36

d)

x2 + +12x - 144

12.

Complete the square.

x2 + 6x + ____

a)

9

b)

12

c)

36

d)

- 9

13.

Complete the square.

x2 - 14x + ____

a)

- 196

b)

49

c)

- 49

d)

28

14.
Find the missing value "c" to create a perfect square trinomial:
x2 + 26x + ___ 
a)
13
b)
136
c)
169
d)
26
15.

Given the perfect square trinomial, identify the equivalent expression


x2-18x+81

a)

(x-18)2

b)

(x-9)2

c)

(x+81)2

d)

(x+9)2

16.

Given the perfect square trinomial, identify the equivalent expression


x2+14x+49

a)

(x+14)2

b)

(x+49)2

c)

(x-7)2

d)

(x+7)2

17.

Find the value of C

x2+5x+c

a)

10

b)

25

c)

25/2

d)

25/4

18.
When factoring
x2 - 4x + 4 = 20,
what goes in the blank?
(x - __ )2 = 20
a)
4
b)
2
c)
8
d)
20
19.
What is the vertex of the parabola?
a)
(-1,0)
b)
(0,-3)
c)
(1,-4)
d)
(3,0)
20.
What is the solution of n2-49=0?
a)
-7
b)
7
c)
± 7
d)
no solution
21.
What are the solutions of the equation x2+8x+15=0?  (Solve by factoring)
a)
-5,-3
b)
-3,5
c)
-5,3
d)
3,5
22.
What is the name of the graph of a quadratic equation?
a)
paramedic
b)
parabola
c)
ebola
d)
parentheses
23.
Identify the 'a' value: y = 16x2 -8x -24
a)
16
b)
8
c)
-8
d)
-24
24.
Identify the 'b' value: y = 16x2 -8x -24
a)
16
b)
-8
c)
8
d)
-24
25.
Use the graph of the function f(x)=-2x2+4x+6 to find the solution(s) of the equation -2x2+4x+6=0.
a)
x=-1
b)
x=3
c)
x=-1 and x=3
d)
x=1and x=8 
26.
What's the axis of symmetry of y = 3x2 - 6x + 4
a)
x=1
b)
x=-6
c)
x=2
d)
x=-1
27.
Find the axis of symmetry of f(x)= -2x2-16x+3.
a)
x= 4
b)
x=-4
c)
y= 4
d)
y=-4
28.
What are the x- intercepts?
a)
x= 0 and x= -4
b)
x= 0 and x= 4
c)
y= 0
d)
x= 2
29.
Find the vertex of the quadratic:
y = -2x2 + 4x + 3
a)
(0, 3)
b)
(-1, 5)
c)
(1, 5)
d)
(1, -5)
30.
Does the equation open up or down? 
Y = -3x2 +7x - 2
a)
up
b)
down
31.

2x2=98

a)

x = 49, x = -49

b)

x = 9.89, x = -9.89

c)

x = 7, x = -7

d)

no solution

32.
a)
-2, 4
b)
-8
c)
±8
d)
No real solution
33.
a)
-3, 4
b)
3, 4
c)
-4, -3
d)
-3
34.
Solve
a2 + 2a - 24 = 0
a)
a = -6, 4
b)
a = 6, -4
c)
a = 12, -2
d)
a = 8, -3
35.
Solve for x.  Round to the nearest hundredth if necessary.
3x2 = 27
a)
x = 9
b)
x = 3
c)
x = -3, 3
d)
x = x = -9, 9
36.
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
37.
Factor
n2-13n+40
a)
(n-5)(n-8)
b)
(n+5)(n-8)
c)
(n-5)(n+8)
d)
(n+6)(n+1)
38.
Solve:  x2 - 81 = 0 
a)
9
b)
9, -9
c)
3, -3, 9, -9
d)
None of the above
39.
Solve: x2+ 6x + 8 = 0
a)
x + 2, x + 4
b)
-2, -4
c)
2, 4
d)
-2, 4
40.

Who is this?

a)

George Jettson

b)

Snoopy

c)

Elmo

d)

Hello Kitty

41.

Who is this?

a)

Mickey Mouse

b)

Minnie Mouse

c)

Scrooge McDuck

d)

Tinkerbell

42.

Describe the image.

a)

Red Tornado

b)

Green Hurricane

c)

Blue Tsunami

d)

Purple Monsoon

43.

Who is this?

a)

SpongeBob

b)

Patrick

c)

Pearl

d)

Gary

Answer Key

Quadratic equation and functions

Total questions: 43

1.
b) a = 4, b =-8, c =-3
2.
b) This is the quadratic formula.
3.
c) 2, -3
4.
c) -8 & 4
5.
c) -5 or 1.5
6.
b) 1
7.
a)

x = 1, 0.75

8.
b) x=2
9.
c)

3, -2

10.
b) divide it by 2 and square the result
11.
b)

x2 + 12x + 36

12.
a)

9

13.
b)

49

14.
c) 169
15.
b)

(x-9)2

16.
d)

(x+7)2

17.
d)

25/4

18.
b) 2
19.
c) (1,-4)
20.
c) ± 7
21.
a) -5,-3
22.
b) parabola
23.
a) 16
24.
b) -8
25.
c) x=-1 and x=3
26.
a) x=1
27.
b) x=-4
28.
b) x= 0 and x= 4
29.
c) (1, 5)
30.
b) down
31.
c)

x = 7, x = -7

32.
a) -2, 4
33.
a) -3, 4
34.
a) a = -6, 4
35.
c) x = -3, 3
36.
a) (x+3)(x+3); x = -3
37.
a) (n-5)(n-8)
38.
b) 9, -9
39.
b) -2, -4
40.
d)

Hello Kitty

41.
d)

Tinkerbell

42.
a)

Red Tornado

43.
d)

Gary

Browse by subjects

Browse by grades

Browse by format

FAQs

What does the Quadratic equation and functions worksheet cover?

This Grade 8 worksheet uses 43 multiple-choice questions to practise identifying a, b, and c in standard-form quadratic equations, solving with the quadratic formula, and determining how many solutions an equation has. It also asks students to complete the square and identify perfect square trinomials, building accuracy across several connected quadratic-equation skills.

How can I use this worksheet to teach quadratic equations and completing the square?

Introduce the worksheet by modelling how to move all terms to one side before identifying a, b, and c, then demonstrate substituting those values into the quadratic formula. Before students complete the completing-the-square items, have them explain why the coefficient of x is divided by 2 and then squared, using examples such as x² + 12x + 36. Review the multiple-choice answers afterward and ask students to justify why the distractors are incorrect.

What mistakes should I watch for when students complete this quadratic formula worksheet?

Watch for students who identify c before rewriting the equation equal to zero, which can reverse its sign, or who substitute the b value incorrectly in the quadratic formula. In the completing-the-square questions, students may divide the x-coefficient by 2 but forget to square the result, especially with negative coefficients such as -14x. Students may also confuse the number of solutions with the number of terms or select an incorrect sign when matching a perfect square trinomial to its squared binomial.

How do I assign and grade this worksheet?

Wayground provides this worksheet as a printable PDF and as a digital quiz, so you can assign the format that fits your Grade 8 math lesson. It includes a complete answer key, and printable submissions can be graded by scanning student work with the Wayground for Teachers app. The printable version can also support schools that are reducing screen time.

How can I differentiate this quadratic equations worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing and font size so the quadratic equations, formula questions, and completing-the-square expressions are easier to read. You can also enable a dyslexia-friendly font or translate the worksheet into another language when appropriate for your learners.

Where can I find more worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across all subjects, with downloadable PDFs and answer keys to help students master essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

© 2026 Wayground Inc.

Accessibility and Inclusion