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Solving Quadratic Equations - Printable Mathematics Worksheets year 11 - Wayground

Solving Quadratic Equations

20 questions

11th - 11th Grade

Mathematics

This Grade 11 mathematics worksheet develops students’ ability to solve quadratic equations using factoring, isolation and square roots, completing the square, and the quadratic formula. Students identify zeros as roots, connect factors with solutions, solve equations with and without a leading coefficient of 1, and recognize when different solution methods apply. The 20-question set includes 17 multiple-choice questions, one ordering task, one drag-and-drop task, and one math-response item. Students sequence the steps for completing the square, complete the quadratic formula, substitute values without simplifying, and interpret solutions that include ± and radicals. This free printable worksheet includes a complete answer key for checking student work and supporting instruction or review.

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Worksheets

Solving Quadratic Equations

Total questions: 20

Name
Class
Date
1.
What are the zeros?
a)
x= 0 and x= -4
b)
x= 0 and x= 4
c)
y= 0
d)
x= 2
2.
What is another word for zeros?
a)
y-intercepts
b)
roots
c)
vertex
d)
axis of symmetry
3.
What are the factors AND solutions of x2 + 2x – 3 = 0
a)
(x - 2)(x + 1); x=2, x=-1
b)
(x + 1)(x - 3); x=-1, x=3
c)
(x + 2)(x - 1); x=-2, x=1
d)
(x - 1)(x + 3); x=1, x=-3
4.

Factor and Solve

6x2 + 17x + 12 = 0

a)

x = -4/3, x = -3/2

b)

x = 9, x = 8

c)

x = 4, x = 3

d)

x = -4, x = -3

5.

Factor and Solve

2x² - 3x - 2 = 0

a)

x = 1, x = -1

b)

x = -1/2, x = 2

c)

x = 1/2, x = 2

d)

x = 1/2, x = 1

6.

Solve the following by ISOLATION

4(x−5)2=124\left(x-5\right)^2=12  

a)

(4x+20)2=12\left(4x+20\right)^2=12  

b)

x=5±3x=5\pm\sqrt[]{3}  

c)

x=−5±3x=-5\pm\sqrt[]{3}  

d)

x=5±123x=5\pm\frac{1}{2}\sqrt[]{3}  

7.

Which method do you feel is the best way to solve the following?

x2−3x−54=0x^2-3x-54=0  

a)

Factor

b)

Isolation/Solve with Square Roots

c)

Complete the Square

d)

Quadratic Formula

8.

What are the steps to solving this by completing the square?

a2 + 10a + 21 = 0

a)

Subtract 21 from both sides of the equation

b)

Add 25 to both sides of the equation

c)

Rewrite the left hand side as a (binomial)2

d)

Take the square root of both sides of the equation

e)

Subtract 5 from both sides of the equation

1)
2)
3)
4)
5)
9.

​Complete the quadratic formula

Black question mark ​ (a)  

Blue question mark ​ (b)  

Red question mark ​ (c)  

Choose from the below words

−b-b  

b2−4acb^2-4ac  

2a2a  

bb  

2b−4ac2b-4ac  

b2−4cb^2-4c  

22  

a2a^2  

b2−acb^2-ac  

2b2b  

10.

2x2+8x−7=02x^2+8x-7=0

Use the quadratic formula to type an expression that will yield the solutions to the equation above.

You cannot type ±\pm on the keyboard so instead put +−+-

DO NOT SIMPLIFY ANYTHING. JUST PLUG IN WITH PARENTHESES.

11.

Solve by factoring: x2 = 7x + 18

a)

-7 and -18

b)

9 and 2

c)

9 and -2

d)

2 and 7

12.
Solve Using the Quadratic Formula
 x2 + 4x - 40 = -8
a)
-10 & -4
b)
-4 & 10
c)
-8 & 4
d)
8 & -4
13.

Solve by the Square Root method: x2 = 16

a)

± 4

b)

± 8

c)

4

d)

8

14.

Solve by the Square Root method:

-5x2 = -50

a)

± 5

b)

± 10

c)

± √10

d)

-10

15.

Solve the following quadratics equation by completing the square...


x2 + 4x + 1 = 0

a)

x = -2 ± √3

b)

x = -3 ± √2

c)

x = 2 ± √3

d)

x = 2 ± √2

16.
Solve the equation by completing the square and then finding the roots. 
x2+ 6x - 4 = 36
a)
x = -7, 7
b)
x = 4, -10
c)
x = -4 +- √7
d)
x = 10, -4
17.

Solve by using a method of your choice:

k2 − 12k + 23 = 0

a)

{6 + √13, 6 - √13}

b)

{-6 + √13, -6 - √13}

c)

{6 + √59, 6 - √59}

d)

{-6 + √59, -6 - √59}

18.

Solve (x+5)2−20=0\left(x+5\right)^2-20=0  , and leave your answer in the form p±qp\pm\sqrt[]{q}  

a)

x=−5±20x=-5\pm\sqrt[]{20}  

b)

x=5±20x=5\pm\sqrt[]{20}  

c)

x=5+20x=5+\sqrt[]{20}  

d)

x=−5−20x=-5-\sqrt[]{20}  

19.
Solve the equation: 
5x2 - 35x + 60 = 0
a)
x = 3,  -4
b)
x = -3,  4
c)
x = 3,  4
d)
x = -3,  -4
20.

How many solutions are there?

a)

0

b)

1

c)

2

d)

3

Answer Key

Solving Quadratic Equations

Total questions: 20

1.
b) x= 0 and x= 4
2.
b) roots
3.
d) (x - 1)(x + 3); x=1, x=-3
4.
a)

x = -4/3, x = -3/2

5.
b)

x = -1/2, x = 2

6.
b)

x=5±3x=5\pm\sqrt[]{3}  

7.
n/a
8.
a, b, c, d, e
9.

−b-b  

,

b2−4acb^2-4ac  

,

2a2a  

10.

−(8)+−(8)2−4(2)(−7)2(2)\frac{-\left(8\right)+-\sqrt{\left(8\right)^2-4\left(2\right)\left(-7\right)}}{2\left(2\right)}

11.
c)

9 and -2

12.
c) -8 & 4
13.
a)

± 4

14.
c)

± √10

15.
a)

x = -2 ± √3

16.
b) x = 4, -10
17.
a)

{6 + √13, 6 - √13}

18.
a)

x=−5±20x=-5\pm\sqrt[]{20}  

19.
c) x = 3,  4
20.
a)

0

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FAQs

What does this Solving Quadratic Equations worksheet cover?

This Grade 11 worksheet asks students to solve quadratics by factoring, isolation or square roots, completing the square, and the quadratic formula. Its varied format—17 multiple-choice items plus ordering, drag-and-drop, and math-response tasks—requires students to identify roots, sequence a completing-the-square procedure, complete the quadratic formula, and substitute values into it without simplifying.

How can I use this worksheet to teach the different methods for solving quadratic equations?

Introduce the worksheet by reviewing that zeros and roots refer to the x-values that make a quadratic equal to zero, then model how to choose among factoring, square roots, completing the square, and the quadratic formula. Have students explain the ordered completing-the-square steps and discuss why an equation such as x² = 16 produces both ±4 before they complete the independent questions.

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

Watch for students confusing roots with y-intercepts, reporting factors without converting them into solutions, or making sign errors when factoring expressions such as x² + 2x − 3. Students may also omit the ± when using square roots, misorder the completing-the-square steps, or substitute into the quadratic formula without preserving parentheses and the correct signs.

How do I assign and grade this quadratic equations worksheet?

You can assign this Solving Quadratic Equations worksheet as a printable PDF or as a digital quiz on Wayground. It includes a complete answer key, and printable submissions can be graded by scanning student work with the Wayground for Teachers app.

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 equation-heavy multiple-choice, ordering, and formula-substitution items easier to read. You can also enable a dyslexia-friendly font or translate the worksheet into another language while keeping the practice focused on the four quadratic-solving methods.

Where can I find more free 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.

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