Free Printable WorksheetMathAlgebra IIMath CurriculumA-SSE.3b

ALG2.38 Completing the Square as an Algebraic Tool Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra II Math worksheet provides structured practice on ALG2.38 Completing the Square as an Algebraic Tool. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.38 Completing the Square as an Algebraic Tool - Rewrite quadratics into vertex form and use the result to solve equations, graph functions, or select the correct interpretation of maximum and minimum values. Associated source-listed standards: CCSS A-SSE.3b; F-IF.8a; CA CCSSM A-SSE.3b; F-IF.8a; MA 2017 A-SSE.3b; F-IF.8a; NY NGLS A-SSE.3b; F-IF.8a; 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 ALG2.38 Completing the Square as an Algebraic Tool skill assessments:

Problem 1Difficulty: Mastery
Solve 16x2 - 8x - 1 = 0 by completing the square.
Ax = (1 + 2sqrt(2))/4 and x = (1 - 2sqrt(2))/4
Bx = (2 + sqrt(2))/4 and x = (2 - sqrt(2))/4
Cx = (1 + sqrt(2))/4 and x = (1 - sqrt(2))/4
Dx = (-1 + sqrt(2))/4 and x = (-1 - sqrt(2))/4
Solution & Explanation:Divide by 16 to get x2 - (1/2)x - 1/16 = 0. Then x2 - (1/2)x = 1/16, add 1/16, and get (x - 1/4)2 = 1/8. Taking square roots gives x = 1/4 ± sqrt(2)/4.
Problem 2Difficulty: Mastery
The quadratic y = 4x2 + bx + 7 has vertex x-coordinate -3/2. What is b?
Solution & Explanation:Use x = -b/(2a). With a = 4 and vertex x = -3/2, we get -b/8 = -3/2, so b = 12.
Problem 3Difficulty: Mastery
Which statement is true about y = x2 - 12x + 45?
AThe function has no x-intercepts and a minimum value of 9 at x = 6.
BThe function has x-intercepts 3 and 9 and a maximum value of 9.
CThe function has a minimum value of -9 at x = 6.
DThe function has one x-intercept at x = 6.
Solution & Explanation:Completing the square gives y = (x - 6)2 + 9. The smallest value is 9 at x = 6, so the graph never reaches 0 and has no x-intercepts.

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Frequently Asked Questions

Common questions about printing, using, and solving this worksheet

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QIs this ALG2.38 Completing the Square as an Algebraic Tool worksheet free for teachers and homeschoolers?

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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-SSE.3b (Rewrite quadratics into vertex form and use the result to solve equations, graph functions, or select the correct interpretation of maximum and minimum values. Associated source-listed standards: CCSS A-SSE.3b; F-IF.8a; CA CCSSM A-SSE.3b; F-IF.8a; MA 2017 A-SSE.3b; F-IF.8a; NY NGLS A-SSE.3b; F-IF.8a; TX TEKS Algebra II: §111.40.).

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