x² − 5x + 6 = 0
Show answer
x = 2 or x = 3
Free printable worksheet
Quadratic Formula Practice Worksheet
Fourteen quadratic equations with rational, repeated, and irrational solutions.
Algebra 1Grades 8-114 pagesAnswer key included
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What this worksheet includes
- Fourteen quadratic equations with rational, repeated, and irrational solutions.
- 4-page printable PDF with a complete answer key
- Designed for Grades 8-11 algebra 1 practice
- Available as an immediate free download with no email required
How to use it
Use this quadratic formula practice worksheet for guided practice, independent review, homework, tutoring sessions, or a quick skills check. The spacious layout is designed to leave room for students to show their work rather than guess from crowded answer choices.
After students finish, compare their reasoning with the included answer key. When an answer is incorrect, have the student locate the first step where their work changed direction before trying the problem again.
Who this practice is for
This resource is designed for grades 8-11 students working on algebra 1. Teachers, tutors, homeschool families, and parents can preview the first page before deciding whether the level and spacing fit the student.
Looking for a broader sequence? Browse all Algebra I worksheets.
Topic guide
How to approach quadratic formula practice
The quadratic formula solves ax² + bx + c = 0 using x = (−b ± √(b² − 4ac)) ÷ 2a. It works for every quadratic equation when a, b, and c are identified with their signs.
The discriminant b² − 4ac predicts the solution type before the square root is simplified. A positive discriminant gives two real solutions, zero gives one repeated solution, and a negative value gives complex solutions.
Learning objectives
- Identify a, b, and c accurately
- Evaluate and interpret the discriminant
- Simplify exact quadratic-formula solutions
Skills to review first
- Standard form of a quadratic
- Signed-number arithmetic
- Simplifying square roots
Worked example
Follow the reasoning step by step
Solve 2x² − 3x − 2 = 0.
- Identify a = 2, b = −3, and c = −2.
- Compute the discriminant: (−3)² − 4(2)(−2) = 25.
- Substitute: x = (3 ± 5) ÷ 4.
- Evaluate both cases to obtain x = 2 and x = −½.
Solution: x = 2 or x = −½.
Try before downloading
Three sample problems
Work each problem, then open the answer to check your result.
x² + 4x + 4 = 0
Show answer
x = −2
x² − 2x − 1 = 0
Show answer
x = 1 ± √2
Error check
Common mistakes to watch for
- Using b without its sign
- Dividing only the radical by 2a
- Forgetting the plus-or-minus symbol