Free Printable WorksheetMathAlgebra IMath CurriculumA-SSE.3a–b

ALG1.86 Equivalent Forms of Quadratic Expressions Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra I Math worksheet provides structured practice on ALG1.86 Equivalent Forms of Quadratic Expressions. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG1.86 Equivalent Forms of Quadratic Expressions - Select the form that correctly converts between standard, factored, and vertex forms of a quadratic; Select the statement that correctly interprets what each form reveals about the graph and solutions. (CCSS: A-SSE.3a–b; F-IF.8a; TEKS: §111.39(c)(6)(A–B), (7)(A–C); VA SOL: A.EO.2 c, A.F.2 b–d; FL B.E.S.T.: MA.912.AR.3.4, 3.6–3.7; NY-NGLS: AI-F.IF.8a, AI-A.SSE.*; CA CCSSM: F-IF.8a; MA 2017: HS.F-IF.8a; DoDEA CCRSM; NAEP: Algebra—quadratic relations; NCTM P2A: Practices 7, 8.)

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 ALG1.86 Equivalent Forms of Quadratic Expressions skill assessments:

Problem 1Difficulty: Mastery
Select the factored form equivalent to y = 3(x - 2)2 - 75 and interpret the zeros.
Ay = 3(x - 7)(x + 3), so the zeros are x = 7 and x = -3.
By = 3(x + 7)(x - 3), so the zeros are x = -7 and x = 3.
Cy = 3(x - 2)(x - 75), so the zeros are x = 2 and x = 75.
Dy = (x - 7)(x + 3), so the zeros are x = 7 and x = -3.
Solution & Explanation:Factor 3: 3[(x - 2)2 - 25]. Difference of squares gives 3(x - 7)(x + 3), so the zeros are x = 7 and x = -3.
Problem 2Difficulty: Mastery
A quadratic has factored form y = k(x + 3)(x - 1) and vertex value -8. Which set of equivalent forms is correct?
Ak = 1, so y = (x + 3)(x - 1) and y = (x + 1)2 - 8
Bk = -2, so y = -2(x + 3)(x - 1) and y = -2(x + 1)2 - 8
Ck = 4, so y = 4(x + 3)(x - 1) and y = 4(x + 1)2 - 8
Dk = 2, so y = 2(x + 3)(x - 1) and y = 2(x + 1)2 - 8
Solution & Explanation:The zeros -3 and 1 have midpoint x = -1. At x = -1, y = k(2)(-2) = -4k. Since the vertex value is -8, k = 2, and vertex form is y = 2(x + 1)2 - 8.
Problem 3Difficulty: Mastery
Select the vertex and factored forms equivalent to y = -2x2 - 12x - 10.
Ay = -2(x - 3)2 + 8 and y = -2(x - 1)(x - 5)
By = -2(x + 3)2 - 10 and y = -2(x + 1)(x + 5)
Cy = -2(x + 3)2 + 8 and y = -2(x + 1)(x + 5)
Dy = 2(x + 3)2 - 8 and y = 2(x + 1)(x + 5)
Solution & Explanation:Factor -2: -2(x2 + 6x + 5). The trinomial factors as (x + 1)(x + 5). Completing the square gives -2[(x + 3)2 - 4] = -2(x + 3)2 + 8.

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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-SSE.3a–b (Primary standard selected for prompt fields in this prompt cell: CCSS A-SSE.3a–b. Skill statement in this prompt cell: Select the form that correctly converts between standard, factored, and vertex forms of a quadratic; Select the statement that correctly interprets what each form reveals about the graph and solutions. Associated standards listed with this skill in the curriculum source: CCSS: A-SSE.3a–b; F-IF.8a; TEKS: §111.39(c)(6)(A–B), (7)(A–C); VA SOL: A.EO.2 c, A.F.2 b–d; FL B.E.S.T.: MA.912.AR.3.4, 3.6–3.7; NY-NGLS: AI-F.IF.8a, AI-A.SSE.*; CA CCSSM: F-IF.8a; MA 2017: HS.F-IF.8a; DoDEA CCRSM; NAEP: Algebra—quadratic relations; NCTM P2A: Practices 7, 8. Use this prompt-provided wording as the supporting standard description for this workflow.).

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