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Solve by Quadratic Formula - Printable Mathematics Worksheets - Wayground

Solve by Quadratic Formula

10 questions

9th - 11th Grade

Mathematics

Solve by Quadratic Formula is a free printable mathematics worksheet for students in Grades 9–11. It provides 10 multiple-choice problems that require students to solve quadratic equations with the quadratic formula, including several items that prompt them to first set the equation equal to zero. Some answer choices include “No Solution,” asking students to evaluate the result rather than select only a numerical solution. The worksheet supports practice with organizing an equation, identifying the coefficients needed for the formula, substituting accurately, simplifying the resulting expression, and selecting the correct solution from multiple choices. It can be used for guided practice, independent work, or a quick check of procedural fluency. A complete answer key is included, making this free printable worksheet useful for classroom instruction, homework, and review.

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Worksheets

Solve by Quadratic Formula

Total questions: 10

Name
Class
Date
1.

Solve using the Quadratic Formula:

2x2+7x−15=02x^2+7x-15=0  

a)

x=−1.5, 5x=-1.5,\ 5  

b)

No Solution

c)

x=−5, 1.5x=-5,\ 1.5  

d)

x=0.7, 5x=0.7,\ 5  

2.

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

x2+4x−40=−8x^2+4x-40=-8  

a)

x=−10, −4x=-10,\ -4  

b)

x=−4, 10x=-4,\ 10  

c)

x=−8, 4x=-8,\ 4  

d)

x=−4, 8x=-4,\ 8  

3.

Solve using the Quadratic Formula:

2x2−x−3=02x^2-x-3=0  

a)

x=−32, 1x=-\frac{3}{2},\ 1  

b)

x=−1, 32x=-1,\ \frac{3}{2}  

c)

x=−32, −1x=-\frac{3}{2},\ -1  

d)

x=1, 32x=1,\ \frac{3}{2}  

4.

Solve using the Quadratic Formula:

2x2+2x−12=02x^2+2x-12=0  

a)

x=−2, 3x=-2,\ 3  

b)

x=2, 3x=2,\ 3  

c)

x=−3, 2x=-3,\ 2  

d)

x=−3, −2x=-3,\ -2  

5.

Solve using the Quadratic Formula:

8x2−6x+1=08x^2-6x+1=0  

a)

No Solution

b)

x=0, 1x=0,\ 1  

c)

x=−0.5, −0.25x=-0.5,\ -0.25  

d)

x=0.25, 0.5x=0.25,\ 0.5  

6.

Solve using the Quadratic Formula:

b2+b−56=0b^2+b-56=0  

a)

b=−8, 7b=-8,\ 7  

b)

b=−7, 8b=-7,\ 8  

c)

b=−1.4, 1.8b=-1.4,\ 1.8  

d)

b=−0.5, 2.5b=-0.5,\ 2.5  

7.

Solve using the Quadratic Formula:

2x2−8x−24=02x^2-8x-24=0  

a)

x=−2, 6x=-2,\ 6  

b)

x=−6, 2x=-6,\ 2  

c)

x=2, 4x=2,\ 4  

d)

x=2, 6x=2,\ 6  

8.

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

x2+2x=8x^2+2x=8  

a)

x=−4, 2x=-4,\ 2  

b)

x=−4, −2x=-4,\ -2  

c)

x=2, 4x=2,\ 4  

d)

x=−2, 4x=-2,\ 4  

9.

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

15x2+22x=−815x^2+22x=-8  

a)

x=−23, 45x=-\frac{2}{3},\ \frac{4}{5}  

b)

x=23, −45x=\frac{2}{3},\ -\frac{4}{5}  

c)

x=23, 45x=\frac{2}{3},\ \frac{4}{5}  

d)

x=−23, −45x=-\frac{2}{3},\ -\frac{4}{5}  

10.

Solve using the Quadratic Formula:

x2+6x+9=0x^2+6x+9=0  

a)

x=−3, 3x=-3,\ 3  

b)

x=−3x=-3  

c)

x=3x=3  

d)

No Solution

Answer Key

Solve by Quadratic Formula

Total questions: 10

1.
c)

x=−5, 1.5x=-5,\ 1.5  

2.
c)

x=−8, 4x=-8,\ 4  

3.
b)

x=−1, 32x=-1,\ \frac{3}{2}  

4.
c)

x=−3, 2x=-3,\ 2  

5.
d)

x=0.25, 0.5x=0.25,\ 0.5  

6.
a)

b=−8, 7b=-8,\ 7  

7.
a)

x=−2, 6x=-2,\ 6  

8.
a)

x=−4, 2x=-4,\ 2  

9.
d)

x=−23, −45x=-\frac{2}{3},\ -\frac{4}{5}  

10.
b)

x=−3x=-3  

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FAQs

What does this Solve by Quadratic Formula worksheet cover?

This Grade 9–11 mathematics worksheet contains 10 multiple-choice problems on solving quadratic equations with the quadratic formula. Students practice putting equations into the required form, substituting the coefficients correctly, simplifying, and evaluating choices that include “No Solution” when appropriate.

How can I use this worksheet to teach solving quadratic equations with the formula?

Model one problem by first rewriting the equation so it equals zero, identifying a, b, and c, and then substituting those values into the quadratic formula. Use the worksheet’s equation-to-zero hint as a transition from guided instruction to independent practice, and ask students to explain how each coefficient was identified before they choose an answer.

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

Watch for students applying the formula before moving all terms to one side, misidentifying the coefficients, or losing negative signs when substituting for b or c. In the multiple-choice items, students may also select a numerical result without checking whether the calculation supports a “No Solution” choice.

How do I assign and grade this Solve by Quadratic Formula worksheet?

Wayground provides this worksheet as a printable PDF and as a digital quiz, and it includes a complete answer key for checking the 10 multiple-choice responses. For printable submissions, you can scan student work with the Wayground for Teachers app to grade it efficiently.

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

In the worksheet’s Advanced Settings, adjust font spacing or font size to make the quadratic-equation items easier to read and annotate. You can also enable a dyslexia-friendly font or translate the worksheet into another language while keeping the multiple-choice format and equation-solving practice intact.

Where can I find more worksheets like this on Wayground?

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

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