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Solving Quadratics Using Quadratic Formula - Printable Math Worksheets 11th Grade - Wayground

Solving Quadratics Using Quadratic Formula

Saige La Tour

Created by Saige La Tour

10 questions

11th Grade

Math

Updated Oct 2026

Solving Quadratics Using Quadratic Formula is a Grade 11 mathematics worksheet that builds fluency with the quadratic formula. Students work through 10 items—8 multiple-choice questions and 2 fill-in-the-blank questions—to identify the coefficients a, b, and c, rewrite equations in standard form when needed, substitute values into the formula, and determine quadratic solutions or x-intercepts. The problems include equations presented in different forms, coefficient-identification prompts, and a statement about when the quadratic formula can be used. This free printable worksheet with an answer key supports guided practice, independent work, homework, or a short formative assessment after introducing the quadratic formula. The fill-in-the-blank items require students to enter coefficient values and solution pairs, helping teachers check whether they can complete the process rather than only recognize a multiple-choice answer. It is designed for Grade 11 math students who are developing accuracy with signs, substitution, and interpreting the two solutions of a quadratic equation.

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WaygroundWorksheets

Solving Quadratics Using Quadratic Formula

Total questions: 10

Name
Class
Date
1.

Solve using the quadratic formula...

9x2 = 4 + 7x

a)
Solve using the quadratic formula... 9x 2 = 4 + 7x
b)
Solve using the quadratic formula... 9x 2 = 4 + 7x
c)
Solve using the quadratic formula... 9x 2 = 4 + 7x
d)

No solution

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.
Solve using the quadratic formula.
2x2 - 9x - 35 = 0
a)
x = 7/2, x = -6
b)
x = -5/2, x =5
c)
x = -3/7, x =6
d)
x = -5/2, x = 7
4.
Identify the 'b' value: y = 16x2 -8x -24
a)
16
b)
-8
c)
8
d)
-24
5.
The quadratic equation can be used to solve quadratic equations that cannot be factored.
a)
True
b)
False
6.
Solve using the quadratic formula.
2x2 - 9x - 35 = 0
a)
x = 7/2, x = -6
b)
x = -5/2, x =5
c)
x = -3/7, x =6
d)
x = -5/2, x = 7
7.
Solve using the quadratic formula.
2x2 - 9x - 35 = 0
a)
x = 7/2, x = -6
b)
x = -5/2, x =5
c)
x = -3/7, x =6
d)
x = -5/2, x = 7
8.

x2−5x −14 = 0x^2-5x\ -14\ =\ 0  

Determine the x-intercepts by completing the quadratic formula. 
x= 5 ±(−5)2−4(1)(−14)2(1)x=\ \frac{5\ \pm\sqrt{\left(-5\right)^2-4\left(1\right)\left(-14\right)}}{2\left(1\right)}  

a)

x=5±−312x=\frac{5\pm\sqrt{-31}}{2}  

b)

x = −7, x = 2x\ =\ -7,\ x\ =\ 2  

c)

x = 7, x = −2x\ =\ 7,\ x\ =\ -2  

d)

no solutionno\ solution  

9.

2x2−14x+23 = 02x^2-14x+23\ =\ 0  What is the a, b, and c?
Type your answer: a = ?, b = ?, c = ?

(a)  

10.

x2+3x−10=0x^2+3x-10=0  
Finish the formula to find the solutions.
x = −3 ±492x\ =\ \frac{-3\ \pm\sqrt{49}}{2}  
Type your answer x = ?, x = ?

(a)  

WaygroundAnswer Key

Solving Quadratics Using Quadratic Formula

Total questions: 10

1.
a)
2.
b)

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

3.
d) x = -5/2, x = 7
4.
b) -8
5.
a) True
6.
d) x = -5/2, x = 7
7.
d) x = -5/2, x = 7
8.
c)

x = 7, x = −2x\ =\ 7,\ x\ =\ -2  

9.
a = 2, b = -14, c = 23, a=2, b=-14, c=23, 2, -14, 23, a=2 b=-14 c=23, a = 2 b = -14 c = 23
10.
x = 2, x = -5, x = -5, x = 2, x=-5, x=2, x=2, x=-5, 2, -5

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FAQs

What does this worksheet cover?

This Grade 11 worksheet covers applying the quadratic formula to solve quadratic equations and determine x-intercepts. Across 8 multiple-choice and 2 fill-in-the-blank items, students identify a, b, and c, substitute those values into the formula, complete the calculation, and report the resulting solutions.

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

Use the coefficient-identification items first to model how an equation must be written in standard form and how signs affect a, b, and c. Then have students solve the multiple-choice equations step by step, discussing the ± portion of the formula and connecting the solutions to x-intercepts before assigning the two fill-in-the-blank items for independent practice.

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

Watch for students copying the constant with the wrong sign when moving a term to the standard form, especially in an equation such as 4x² − 8x = 3. Students may also substitute the wrong b value, omit the ± operation, make an arithmetic error under the square root, or enter only one of the two solutions in the fill-in-the-blank response.

How do I assign and grade this worksheet?

This worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key. You can grade printable submissions by scanning student work with the Wayground for Teachers app, while the digital quiz provides an online way to assign the same quadratic-formula practice.

Why does this worksheet ask students to identify a, b, and c before solving?

The coefficient-identification questions prepare students to use the quadratic formula accurately, because every substitution depends on recognizing the correct a, b, and c values and their signs. The worksheet then applies that prerequisite to solving equations and finding x-intercepts, so teachers can see whether an error comes from reading the equation or from carrying out the formula.

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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