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The Quadratic Formula - Printable Mathematics Worksheets - Wayground

The Quadratic Formula

10 questions

9th - 11th Grade

Mathematics

The Quadratic Formula worksheet helps students in Grades 9–11 identify the values of a, b, and c, rewrite quadratic equations in standard form, and apply the quadratic formula accurately. Across 10 multiple-choice questions, students also identify the discriminant, determine the number of zeros of a parabola, find solutions to quadratic equations, and connect solutions to x-intercepts. This free printable mathematics worksheet gives students focused practice with both the setup and computation required for quadratic-formula problems. The questions address common decision points, including setting an equation equal to zero, interpreting the discriminant, selecting correct solutions, and recognizing x-intercepts from calculated roots. An answer key is included for efficient review, independent practice, or formative assessment.

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Worksheets

The Quadratic Formula

Total questions: 10

Name
Class
Date
1.

What is the "a" value needed for the quadratic formula in the equation y = x2 − 6x + 3y\ =\ x^2\ -\ 6x\ +\ 3  .

a)

-6

b)

3

c)

1

d)

0

2.

Determine the values of

a, b, and c for

the quadratic equation:

4x2 – 8x = 3

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

3.

Do you need to set the equation equal to zero before starting The Quadratic Formula?

a)

Yes!

b)

Only if you want to.

c)

No!

4.
The discriminant is
a)
aX2  + bX  +  c
b)
b - 4ac
c)
b2 - 4ac
d)
b2 + 4ac
5.
How many zeros does this parabola have? 
a)
3
b)
2
c)
0
d)
1
6.

Use the quadratic formula to solve 2x2 + 2x - 12=0

a)

-2 and 3

b)

2 and 3

c)

2 and -3

d)

-2 and -3

7.

Using the quadratic formula, find the x-intercepts for the graph of y = x2 − 4x − 32y\ =\ x^2\ -\ 4x\ -\ 32  .

a)

(8, 0) and (-4, 0)

b)

(4, 0) and (-8, 0)

c)

(74, 0) and (-70, 0)

d)

(70, 0) and (-74, 0)

8.

When solving using the quadratic formula, which equation would give you the x-intercepts BEFORE calculating the square root for the equation y = 3x2−2x−4y\ =\ 3x^2-2x-4  

a)

x=−2±526x=\frac{-2\pm\sqrt[]{52}}{6}  

b)

x=2±−446x=\frac{2\pm\sqrt[]{-44}}{6}  

c)

x=2±526x=\frac{2\pm\sqrt[]{52}}{6}  

d)

x=2±−442x=\frac{2\pm\sqrt[]{-44}}{2}  

9.

Solve by the Quadratic Formula:

9u2−11u+7=09u^2-11u+7=0  

a)

−11±13118\frac{-11\pm\sqrt{131}}{18}  

b)

11±13118\frac{11\pm\sqrt{131}}{18}  

c)

11±131−18\frac{11\pm\sqrt{131}}{-18}  

d)

11±i37318\frac{11\pm i\sqrt{373}}{18}  

10.
Solve the quadratic equation.
3x2 - 8x - 8 = 0
a)
A    {0.38, -0.88} 
b)
B  {0.89, -8.9}
c)
C . {0.13, -0.63}
d)
D . {3.44, -0.77}
Answer Key

The Quadratic Formula

Total questions: 10

1.
c)

1

2.
b)

a = 4, b =-8, c =-3

3.
a)

Yes!

4.
c) b2 - 4ac
5.
b) 2
6.
c)

2 and -3

7.
a)

(8, 0) and (-4, 0)

8.
c)

x=2±526x=\frac{2\pm\sqrt[]{52}}{6}  

9.
b)

11±13118\frac{11\pm\sqrt{131}}{18}  

10.
d) D . {3.44, -0.77}

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FAQs

What does this quadratic formula worksheet cover?

This Grade 9–11 mathematics worksheet uses 10 multiple-choice questions to practice identifying a, b, and c, rewriting equations in standard form, using the discriminant, and solving quadratic equations with the quadratic formula. Students also connect the resulting roots to the number of zeros and the x-intercepts of a parabola, building accuracy from setup through interpretation.

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

Begin by modeling how to rewrite an equation such as 4x² − 8x = 3 so it equals zero before identifying a, b, and c. Then use the worksheet’s questions on the discriminant, zeros, roots, and x-intercepts in sequence, asking students to explain why a selected answer matches each step of the quadratic formula. Finish by having students check whether their calculated roots agree with the graph or intercepts described in the questions.

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

Watch for students identifying c as 3 instead of −3 after moving 3 to the left side of 4x² − 8x = 3, or using the wrong sign in b² − 4ac. Students may also substitute coefficients before setting the equation equal to zero, confuse roots with x-intercepts, or select incorrect decimal solutions after evaluating the formula. Reviewing the relationship between roots, zeros, and points written as (x, 0) can help expose these errors.

How do I assign and grade this quadratic formula worksheet?

The worksheet is available on Wayground as a printable PDF and as a digital quiz, and it includes a complete answer key for checking the 10 multiple-choice questions. For printable submissions, you can scan student work with the Wayground for Teachers app to streamline grading. The PDF option also supports classrooms that want to reduce screen time while students practice identifying coefficients and solving quadratic equations.

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

Use the worksheet’s Advanced Settings to adjust font spacing and font size so the coefficient-identification and formula-substitution items are easier to read. You can also enable a dyslexia-friendly font or translate the worksheet into another language when those options support access to the quadratic-formula questions.

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.

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