Free Printable WorksheetMathAlgebra IMath CurriculumA-REI.4a–b

ALG1.91 Discriminant and Number of Real Solutions Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra I Math worksheet provides structured practice on ALG1.91 Discriminant and Number of Real Solutions. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG1.91 Discriminant and Number of Real Solutions - Select the option that shows how to use the discriminant to determine the number of real solutions to a quadratic equation; Select the statement that correctly interprets what each case means for the graph’s x-intercepts. (CCSS: A-REI.4a–b; TEKS: §111.39(c)(6)(A–C); VA SOL: A.EI.3 a–c; FL B.E.S.T.: MA.912.AR.3.1, 3.8; NY-NGLS: AI-A.REI.4a–b; CA CCSSM: A-REI.4; MA 2017: HS.A-REI.4; DoDEA CCRSM; NAEP: Algebra—equations; NCTM P2A: Practices 1, 6.)

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 I

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 ALG1.91 Discriminant and Number of Real Solutions skill assessments:

Problem 1Difficulty: Mastery
Which option fully explains why 5x2 + 10x + 8 = 0 has no real solutions?
AD = 52 - 4(10)(8) = -295, so the equation has one repeated real solution.
BD = 102 - 4(8)(5) = -60, so the graph crosses the x-axis twice.
CD = 102 + 4(5)(8) = 260, so the square root part is positive and the graph has no x-intercepts.
DD = 102 - 4(5)(8) = -60, so the square root part of the quadratic formula is not real and the graph has no x-intercepts.
Solution & Explanation:Use a = 5, b = 10, and c = 8. D = 100 - 160 = -60. Because the discriminant is negative, there are no real solutions and no x-intercepts.
Problem 2Difficulty: Mastery
A vertical shift changes h(x) = x2 - 6x + 8 into h(x) + k. Which value of k makes the shifted graph have no x-intercepts?
Ak = 2
Bk = -3
Ck = 0
Dk = 1
Solution & Explanation:The shifted equation is x2 - 6x + (8 + k) = 0. D = (-6)2 - 4(1)(8 + k) = 36 - 32 - 4k = 4 - 4k. No x-intercepts require D < 0, so k > 1. The choice k = 2 works.
Problem 3Difficulty: Mastery
The graph shown is an upward-opening parabola with vertex at (2, -3). Which discriminant statement is correct?
AD cannot be connected to x-intercepts.
BD = 0 because the graph's vertex is visible.
CD < 0 because the graph has no x-intercepts.
DD > 0 because the graph crosses the x-axis twice.
Solution & Explanation:An upward-opening parabola with its vertex below the x-axis crosses the x-axis twice. Two x-intercepts mean two real solutions and D > 0.

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Algebra I Math students. It aligns with educational standard A-REI.4a–b (Primary standard selected for prompt fields in this prompt cell: CCSS A-REI.4a–b. Skill statement in this prompt cell: Select the option that shows how to use the discriminant to determine the number of real solutions to a quadratic equation; Select the statement that correctly interprets what each case means for the graph’s x-intercepts. Associated standards listed with this skill in the curriculum source: CCSS: A-REI.4a–b; TEKS: §111.39(c)(6)(A–C); VA SOL: A.EI.3 a–c; FL B.E.S.T.: MA.912.AR.3.1, 3.8; NY-NGLS: AI-A.REI.4a–b; CA CCSSM: A-REI.4; MA 2017: HS.A-REI.4; DoDEA CCRSM; NAEP: Algebra—equations; NCTM P2A: Practices 1, 6. Use this prompt-provided wording as the supporting standard description for this workflow.).

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