The Discriminant - Worksheet 9 - 9th Grade
HardUse the discriminant to determine the nature of solutions (Hard)
23 problems · 15-20 minutes · Skills: quadratics, discriminant, algebra
About This Worksheet
This hard-level worksheet contains 23 problems designed for 9th Grade students practicing the discriminant. Hard worksheets feature challenging problems including multi-step questions, missing values, and real-world applications to push students further.
The discriminant provides instant insight into the nature of solutions without solving the entire equation. This efficiency is valuable in applied mathematics, and the concept of using a derived quantity to classify solutions generalizes throughout advanced mathematics.
- Calculate the discriminant b² − 4ac from a quadratic in standard form
- Determine whether a quadratic has two real, one real, or no real solutions
- Connect the discriminant to the number of x-intercepts on a parabola's graph
- Use the discriminant to decide which solving method to apply before attempting a solution
- Identify the discriminant value that indicates a perfect square trinomial
How to Solve: Worked Example
- b² - 4ac = 400 - 4(2)(50) = 400 - 400 = 0.
- A zero discriminant means exactly one real solution.
- That root is repeated — the parabola touches the x-axis at a single point.
Answer Key
Frequently Asked Questions
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What skills does this quadratic functions worksheet cover?
This worksheet focuses on quadratics, discriminant, algebra. It is designed for 9th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.
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How many problems are on this worksheet?
This worksheet contains 23 problems. It typically takes 15-20 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.