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Quadratic Formula Review - Printable Mathematics Worksheets - Wayground

Quadratic Formula Review

20 questions

11th - 11th Grade

Mathematics

Quadratic Formula Review is a Grade 11 mathematics worksheet focused on using the quadratic formula to solve quadratic equations and determine the nature of their roots. Students identify the quadratic formula, calculate discriminants, classify root types, find real or complex solutions, and simplify final answers. The worksheet includes 20 questions: 17 multiple-choice items, two math-response questions, and one fill-in-the-blank item. This free printable worksheet gives students repeated practice connecting the discriminant to the number and type of roots rather than applying the quadratic formula mechanically. It is suitable for review, independent practice, homework, or a formative check after instruction on quadratic equations. A complete answer key is included so teachers can quickly verify students’ calculations and use errors to revisit coefficient identification, discriminant evaluation, substitution, and simplification.

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Worksheets

Quadratic Formula Review

Total questions: 20

Name
Class
Date
1.

Use the quadratic formula to find the solutions for

y = -x2 - 5x + 12

a)

No Real Solution

b)
c)
d)
2.

What is the quadratic formula?

a)
b)
c)
d)
3.
a)

A

b)

B

c)

C

d)

D

4.

____________
For the function above, is the discriminant positive, negative, or zero?

a)

Positive

b)

Negative

c)

Zero

d)

Not Sure

5.

____________
For the function above, is the discriminant positive, negative, or zero?

a)

Positive

b)

Negative

c)

Zero

d)

Not Sure

6.

Solve the quadratic equation 2x2−4x−6=02x^2 - 4x - 6 = 0 using the quadratic formula.

a)

x=3,x=−1x = 3, x = -1

b)

x=2,x=−3x = 2, x = -3

c)

x=2,x=−1x = 2, x = -1

d)

x=3,x=−2x = 3, x = -2

7.

Determine the nature of the roots for the equation x2+4x+5=0x^2 + 4x + 5 = 0 by analyzing the discriminant.

a)

Two distinct real roots

b)

One real root

c)

Two complex roots

d)

No roots

8.

Find the real roots of the equation 3x2−12x+9=03x^2 - 12x + 9 = 0 using the quadratic formula.

a)

x=1,x=3x = 1, x = 3

b)

x=2,x=1x = 2, x = 1

c)

x=1x = 1

d)

x=2x = 2

9.

What is the discriminant of the quadratic equation x2−6x+9=0x^2 - 6x + 9 = 0 ?

a)

0

b)

9

c)

36

d)

-9

10.

Solve for the roots of the equation x2+2x−8=0x^2 + 2x - 8 = 0 using the quadratic formula.

a)

x=2,x=−4x = 2, x = -4

b)

x=4,x=−2x = 4, x = -2

c)

x=3,x=−3x = 3, x = -3

d)

x=4,x=2x = 4, x = 2

11.

For the equation 5x2+2x+1=05x^2 + 2x + 1 = 0 , determine the nature of the roots by analyzing the discriminant.

a)

Two distinct real roots

b)

One real root

c)

Two complex roots

d)

No roots

12.

Calculate the roots of the quadratic equation x2−5x+6=0x^2 - 5x + 6 = 0 using the quadratic formula.

a)

x=2,x=3x = 2, x = 3

b)

x=1,x=6x = 1, x = 6

c)

x=3,x=−2x = 3, x = -2

d)

x=2,x=−3x = 2, x = -3

13.

What is the discriminant of the quadratic equation 2x2+3x+1=02x^2 + 3x + 1 = 0 ?

a)

1

b)

5

c)

0

d)

-7

14.

Solve the quadratic equation x2−4x+4=0x^2 - 4x + 4 = 0 using the quadratic formula.

a)

x=2x = 2

b)

x=4x = 4

c)

x=0x = 0

d)

x=−2x = -2

15.

Determine the nature of the roots for the equation 4x2−4x+1=04x^2 - 4x + 1 = 0 by analyzing the discriminant.

a)

Two distinct real roots

b)

One real root

c)

Two complex roots

d)

No roots

16.

x2+5x +8 =0x^2+5x\ +8\ =0  

Solve the given equation using the Quadratic Formula. Make sure you fully simplify your answer.

a)

−5±572\frac{-5\pm\sqrt{57}}{2}  

b)

5±572\frac{5\pm\sqrt{57}}{2}  

c)

−5±i72\frac{-5\pm i\sqrt{7}}{2}  

d)

5±i72\frac{5\pm i\sqrt{7}}{2}  

17.

What is the discriminant of the quadratic equation x2+6x+9=0x^2 + 6x + 9 = 0 ?

18.

What are the solutions to the following equation?

(a)  

19.

Practice Problem 9

smaller of the two answers only

Type your answer as x= with no extra spaces

20.


a2−22a+ca^2-22a+c  is a quadratic expression in standard form.  Find the "magic number"  c=(b2)2c=\left(\frac{b}{2}\right)^2  that makes the expression a perfect-square trinomial, and "completes the square".

a)

-121

b)

121

c)

11

d)

-11

Answer Key

Quadratic Formula Review

Total questions: 20

1.
b)
2.
a)
3.
c)

C

4.
b)

Negative

5.
c)

Zero

6.
a)

x=3,x=−1x = 3, x = -1

7.
d)

No roots

8.
a)

x=1,x=3x = 1, x = 3

9.
a)

0

10.
b)

x=4,x=−2x = 4, x = -2

11.
c)

Two complex roots

12.
a)

x=2,x=3x = 2, x = 3

13.
a)

1

14.
a)

x=2x = 2

15.
b)

One real root

16.
c)

−5±i72\frac{-5\pm i\sqrt{7}}{2}  

17.

00

18.
x=1/5 x=-3
19.

x=−1x=-1

20.
b)

121

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FAQs

What does the Quadratic Formula Review worksheet cover?

This Grade 11 mathematics worksheet practices identifying and applying the quadratic formula, calculating the discriminant, classifying the roots, and simplifying solutions to quadratic equations. Its 20 items combine multiple-choice questions with math-response and fill-in-the-blank tasks, requiring students to move from recognizing the formula to finding and interpreting solutions.

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

First model how to identify a, b, and c, calculate the discriminant, and substitute each value into the quadratic formula. Then use the worksheet’s sequence of formula-identification, discriminant-classification, and equation-solving questions to have students explain why a positive, zero, or negative discriminant leads to different root types before completing the independent-response items.

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

Watch for students copying a negative coefficient incorrectly, especially when identifying b or calculating b² − 4ac. Students may also confuse the discriminant’s value with the roots themselves, misclassify the number or type of roots, or stop before fully simplifying a solution. The math-response and fill-in-the-blank items can reveal these process errors more clearly than the multiple-choice questions.

How do I assign and grade this quadratic formula worksheet?

On Wayground, assign it as a printable PDF or as a digital quiz. The worksheet includes a complete answer key, and printable submissions can be graded by scanning student work with the Wayground for Teachers app. The PDF option also supports classrooms that want to reduce screen time while students work through the quadratic-formula and discriminant questions.

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 equation-solving items and written responses have the visual space students need. You can also apply a dyslexia-friendly font or translate the worksheet into another language, which may make the quadratic-formula directions and root-classification choices easier to access.

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 mastery of essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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