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Quadratic Equations and Functions

20 questions

10th - 10th Grade

Mathematics

Quadratic Equations and Functions is a Grade 10 mathematics worksheet that builds fluency with solving and interpreting quadratic equations. Its 20 multiple-choice questions ask students to identify a parabola’s minimum point, complete the square, rewrite equations in vertex or factored form, solve by factoring and the quadratic formula, and use a graph to identify solutions. The worksheet also checks students’ understanding of the discriminant, including how its value indicates whether a quadratic has zero, one, or two real solutions. It is useful for guided practice, independent review, or a formative assessment after instruction on quadratic functions. This free printable worksheet includes a complete answer key so teachers can quickly review students’ choices and identify which algebraic methods need reinforcement.

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Worksheets

Quadratic Equations and Functions

Total questions: 20

Name
Class
Date
1.
Find the minimum point of the graph x2 + 12x + 4
a)
( -12 , -32 ) 
b)
( -6 , -32 ) 
c)
( -6 , 32 ) 
d)
( 12 , -14 ) 
2.
Complete the Square
x2 + 6x + 20
a)
(x + 3x)2 + 11
b)
(x + 3)2 + 11
c)
(x + 6)2 + 11
d)
(x + 3)2 + 29
3.
Solve
16a2 - 9 = 0
a)
a = -3/4, 3/4 
b)
a = -4/3, 4/3 
c)
a = -9/16, 9/16 
d)
a = -16/9, 16/9 
4.
Solve
a2 + 2a - 24 = 0
a)
a = -6, 4
b)
a = 6, -4
c)
a = 12, -2
d)
a = 8, -3
5.
When factoring
x2 - 4x + 4 = 20,
what goes in the blank?
(x - __ )2 = 20
a)
4
b)
2
c)
8
d)
20
6.
Solve
8n2 + 10n - 3 = 0
a)
n = -1/8, 10/3
b)
n = 4/5, - 2
c)
n = 1/4, -3/2
d)
n = 2, -12
7.
Solve by using the quadratic formula:
15x2+22x=-8
a)
-2/3, 4/5
b)
2/3, -4/5
c)
2/3, 4/5
d)
-2/3, -4/5
8.
Write the equation in vertex form: 
y = x2 + 10x + 20
a)
y=(x+5)2 + 5
b)
y=(x+5)2 + 45
c)
y=(x+5)2 + 20
d)
y=(x+5)2 - 5
9.
Use the graph to determine the solutions.
a)
-1 and -3
b)
1 and -3
c)
1 and 3
d)
-1 and 3
10.
Solve the equation by factoring:
x2-6x+8=0
a)
2, 4
b)
-2, -4
c)
-2, 4
d)
2, -4
11.
Rewrite this quadratic in factored form:
x2- 15 = 1
a)
(x - 4)(x + 4)
b)
(x - 4)(x - 4) 
c)
(x + 4) (x + 4) 
d)
(x - 8)(x + 2) 
12.
a)
±72
b)
±12
c)
12
d)
No real solution
13.
What is the discriminant?
a)
b²-4ac
b)
b2/2a
c)
4ac
d)
b2±4ac
14.
If the discriminant equals 0, then the quadratic has:
a)
1 Real Solution
b)
2 Real Solutions
c)
Half a Solution
d)
No Real Solution
15.
If the discriminant is negative, then the quadratic has:
a)
1 Real Solution
b)
2 Real Solutions
c)
Half a Solution
d)
No Real Solutions
16.
If the discriminant is positive, then the quadratic has:
a)
1 Real Solution
b)
2 Real Solutions
c)
Half a Solution
d)
No Real Solution
17.
If the graph of a quadratic does not intercept the x axis at any point, then it has:
a)
1 Real Solution
b)
2 Real Solutions
c)
Half a Solution
d)
No Real Solution
18.
Which method is best for solving the equation 8x2-13x+3=0?
a)
square roots
b)
factoring
c)
graphing
d)
quadratic formula
19.
The product of two consecutive integers, n and n+1, is 42. What is the positive integer that satisfies the situation?
a)
7
b)
6
c)
21
d)
2
20.
b2 - 4ac would equal: y = 2x2 -x -3
a)
25
b)
-23
c)
-25
d)
0
Answer Key

Quadratic Equations and Functions

Total questions: 20

1.
b) ( -6 , -32 ) 
2.
b) (x + 3)2 + 11
3.
a) a = -3/4, 3/4 
4.
a) a = -6, 4
5.
b) 2
6.
c) n = 1/4, -3/2
7.
d) -2/3, -4/5
8.
d) y=(x+5)2 - 5
9.
c) 1 and 3
10.
a) 2, 4
11.
a) (x - 4)(x + 4)
12.
d) No real solution
13.
a) b²-4ac
14.
a) 1 Real Solution
15.
d) No Real Solutions
16.
b) 2 Real Solutions
17.
d) No Real Solution
18.
d) quadratic formula
19.
b) 6
20.
a) 25

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FAQs

What does this quadratic equations worksheet help Grade 10 students learn?

This worksheet uses 20 multiple-choice questions to practise several connected quadratic skills: finding a parabola’s minimum point, completing the square, rewriting equations in vertex and factored form, and solving equations by factoring or the quadratic formula. Students also interpret graph-based solutions and use the discriminant to determine whether a quadratic has zero, one, or two real solutions. Selecting among worked-result options reinforces both procedural accuracy and interpretation of quadratic functions.

How can I use this worksheet to teach quadratic equations and functions?

Use the questions in a progression: begin with completing the square and vertex form, then connect those forms to the minimum point of a parabola. Follow with factoring and quadratic-formula items, asking students to explain why each method fits the equation before choosing an answer. Finish with the graph and discriminant questions to discuss how algebraic solutions correspond to x-intercepts and the number of real solutions.

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

Students may use the wrong sign or half the coefficient when completing the square, which can produce an incorrect vertex form or minimum point. They may also lose a root when factoring, substitute incorrectly in the quadratic formula, or confuse the discriminant rules: zero gives one real solution, a positive value gives two, and a negative value gives none. In the graph item, check that students identify the x-intercepts rather than another point on the parabola.

How do I assign and grade this quadratic equations worksheet?

The worksheet is available on Wayground as a printable PDF and as a digital quiz, with a complete answer key for all 20 multiple-choice questions. You can grade printable submissions by scanning student work with the Wayground for Teachers app, or review responses from the digital version.

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

In the worksheet’s Advanced Settings, adjust font spacing or choose a larger font size to make the multiple-choice equations, fractions, and answer options easier to read. You can also enable a dyslexia-friendly font or translate the worksheet text into another language while retaining the quadratic practice format.

Where can I find more worksheets like this on Wayground?

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

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