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

ALG1.89 Solve Quadratic Equations by Square Roots and Quadratic Formula Answer Key Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra I Math worksheet provides structured practice on ALG1.89 Solve Quadratic Equations by Square Roots and Quadratic Formula Answer Key. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG1.89 Solve Quadratic Equations by Square Roots and Quadratic Formula - Select the correct solution to quadratic equations by taking square roots or using the quadratic formula; Select the statement that correctly interprets the solutions and connect them to the graph of the quadratic. (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 ALG1.89 Solve Quadratic Equations by Square Roots and Quadratic Formula Answer Key skill assessments:

Problem 1Difficulty: Mastery
For 3x2 - 10x - 8 = 0, the quadratic formula gives x = (10 plus or minus sqrt(196))/6. Which graph statement matches the solutions?
AThe graph touches the x-axis at x = 10/6
BThe graph has no x-intercepts
CThe graph crosses the x-axis at x = 2/3 and x = -4
DThe graph crosses the x-axis at x = -2/3 and x = 4
Solution & Explanation:Since sqrt(196) = 14, x = (10 plus or minus 14)/6. This gives x = 4 and x = -2/3, so those x-values are the x-intercepts.
Problem 2Difficulty: Mastery
A graph of y = -3(x - 1)2 + 12 is shown. Which statement correctly connects the graph to the equation y = 0?
AThe solutions are x = 1 and x = 12, the vertex coordinates
BThere are no real solutions because the graph opens downward
CThe solutions are x = -1 and x = 3, the x-intercepts
DThe only solution is x = 1
Solution & Explanation:Set -3(x - 1)2 + 12 = 0. Then (x - 1)2 = 4, so x = -1 or x = 3; these are the two x-intercepts shown on the graph.
Problem 3Difficulty: Mastery
Which square-root equation has solutions x = -2 + sqrt(6) and x = -2 - sqrt(6)?
A(x + 2)2 = 6
Bx2 = -2 + sqrt(6)
C(x - 2)2 = 6
D(x + 6)2 = 2
Solution & Explanation:If x = -2 plus or minus sqrt(6), then x + 2 = plus or minus sqrt(6). Squaring both sides gives (x + 2)2 = 6.

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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 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 correct solution to quadratic equations by taking square roots or using the quadratic formula; Select the statement that correctly interprets the solutions and connect them to the graph of the quadratic. 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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