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

ALG1.87 Complete the Square and Vertex Form Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra I Math worksheet provides structured practice on ALG1.87 Complete the Square and Vertex Form. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG1.87 Complete the Square and Vertex Form - Select the completed form of the square to rewrite a quadratic in vertex form; Select the option that shows how to use vertex form to identify the vertex and to graph efficiently. (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 ALG1.87 Complete the Square and Vertex Form skill assessments:

Problem 1Difficulty: Mastery
Which option correctly completes the square and interprets y = -5x2 + 30x - 40?
Ay = -5(x + 3)2 + 5, so the maximum is 5 at x = -3.
By = -5(x - 3)2 - 40, so the maximum is -40 at x = 3.
Cy = 5(x - 3)2 + 5, so the minimum is 5 at x = 3.
Dy = -5(x - 3)2 + 5, so the maximum is 5 at x = 3.
Solution & Explanation:Factor -5: -5(x2 - 6x) - 40 = -5[(x - 3)2 - 9] - 40 = -5(x - 3)2 + 5.
Problem 2Difficulty: Mastery
Which set of graph features matches y = (x + 1)2 - 4?
AVertex (1, -4), x-intercepts -3 and 1, opens up.
BVertex (-1, 4), x-intercepts -3 and 1, opens down.
CVertex (-1, -4), x-intercepts -3 and 1, opens up.
DVertex (-1, -4), x-intercepts 3 and -1, opens up.
Solution & Explanation:The vertex is (-1, -4). Setting (x + 1)2 - 4 = 0 gives (x + 1)2 = 4, so x = -3 or x = 1. The positive leading coefficient means it opens up.
Problem 3Difficulty: Mastery
The point (0, 0) lies on y = -3(x + 2)2 + 12. What other point on the graph is symmetric with it?
A(4, 0)
B(-4, 0)
C(-2, 0)
D(0, -4)
Solution & Explanation:The axis of symmetry is x = -2. The point (0, 0) is 2 units to the right of the axis, so its symmetric point is 2 units to the left at x = -4 with the same y-value.

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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-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 completed form of the square to rewrite a quadratic in vertex form; Select the option that shows how to use vertex form to identify the vertex and to graph efficiently. 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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