Free Printable WorksheetMathAlgebra IIMath CurriculumA-REI.11–12

ALG2.96 Quadratic Inequalities Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra II Math worksheet provides structured practice on ALG2.96 Quadratic Inequalities. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.96 Quadratic Inequalities - Select the correct solution(s) to quadratic inequalities using graphs and sign analysis, and express solution sets using interval notation. Associated source-listed standards: CCSS A-REI.11–12; CA CCSSM A-REI.11–12; MA 2017 A-REI.11–12; NY NGLS A-REI.11–12; TX TEKS Algebra II: §111.40.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Algebra II

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related ALG2.96 Quadratic Inequalities skill assessments:

Problem 1Difficulty: Mastery

A quadratic has zeros at 2 and 7 and opens upward. Which interval solves f(x) > 0?

A(-∞, 2] U [7, ∞)

B(2, 7)

C(-∞, 2) U (7, ∞)

D[2, 7]

Solution & Explanation:An upward-opening parabola is positive outside its zeros and negative between them. Because the inequality is strict, exclude the zeros. The solution set is (-∞, 2) U (7, ∞).

Problem 2Difficulty: Mastery

Solve -2(x - 3)(x + 1) ≤ 4. Which interval notation is correct?

A(1 - sqrt(2), 1 + sqrt(2))

B(-∞, 1 - sqrt(2)) U (1 + sqrt(2), ∞)

C[1 - sqrt(2), 1 + sqrt(2)]

D(-∞, 1 - sqrt(2)] U [1 + sqrt(2), ∞)

Solution & Explanation:Move everything to one side: -2(x - 3)(x + 1) ≤ 4 becomes -2x² + 4x + 2 ≤ 0. The zeros are 1 - sqrt(2) and 1 + sqrt(2). The parabola opens downward, so the expression is positive between the zeros and negative outside them. Include the zeros because the inequality is ≤ 0. The solution set is (-∞, 1 - sqrt(2)] U [1 + sqrt(2), ∞).

Problem 3Difficulty: Mastery

A design score is modeled by S(p) = -(p - 4)² + 25. For which parameter values is the score at most 9?

A(-∞, 0] U [8, ∞)

B[0, 8]

C(-∞, 0) U (8, ∞)

D(0, 8)

Solution & Explanation:Set -(p - 4)² + 25 ≤ 9 and move the threshold to one side: -p² + 8p ≤ 0. The zeros are 0 and 8. The parabola opens downward, so the expression is positive between the zeros and negative outside them. Include the zeros because the inequality is ≤ 0. The solution set is (-∞, 0] U [8, ∞).

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Frequently Asked Questions

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Algebra II Math students. It aligns with educational standard A-REI.11–12 (Select the correct solution(s) to quadratic inequalities using graphs and sign analysis, and express solution sets using interval notation. Associated source-listed standards: CCSS A-REI.11–12; CA CCSSM A-REI.11–12; MA 2017 A-REI.11–12; NY NGLS A-REI.11–12; TX TEKS Algebra II: §111.40.).