Free Printable WorksheetMathGeometryMath CurriculumG-GPE.A.1

GEO.151 Complete the square to rewrite circle equations Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.151 Complete the square to rewrite circle equations. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.151 Complete the square to rewrite circle equations - Primary standard selected for prompt fields in this prompt cell: CCSS G-GPE.A.1. Skill statement in this prompt cell: Select the correctly completed-square form of a given circle equation and identify the corresponding center and radius. Associated standards listed with this skill in the curriculum source: CCSS G-GPE.A.1; FL MA.912.GR.7.2-7.3; VA G.PC.4; TEKS §111.41(c). Use this prompt-provided wording as the supporting standard description for this workflow.

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

Geometry

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 GEO.151 Complete the square to rewrite circle equations skill assessments:

Problem 1Difficulty: Mastery

For a mastery check on completing the square, which option correctly rewrites x² + y² - 32x - 48y = 129 and names the circle's key features?

ACompleted form: (x + 16)² + (y + 24)² = 961; center (-16, -24); radius 31

BCompleted form: (x - 16)² + (y - 24)² = 1793; center (16, 24); radius sqrt(1793)

CCompleted form: (x - 32)² + (y - 48)² = 961; center (32, 48); radius 31

DCompleted form: (x - 16)² + (y - 24)² = 961; center (16, 24); radius 31

Solution & Explanation:Group the x-terms and y-terms, then add 256 to complete the x-square and 576 to complete the y-square. This gives (x - 16)² + (y - 24)² = 961. In standard form (x-h)²+(y-k)²=r², the center is (16, 24) and the radius is 31.

Problem 2Difficulty: Mastery

A common wrong answer for x² + 56x + y² - 8y - 41 = 0 uses the opposite center. Which option gives the correct center and radius?

ACompleted form: (x - 28)² + (y + 4)² = 841; center (28, -4); radius 29

BCompleted form: (x + 28)² + (y - 4)² = 1641; center (-28, 4); radius sqrt(1641)

CCompleted form: (x + 28)² + (y - 4)² = 841; center (-28, 4); radius 29

DCompleted form: (x + 56)² + (y - 8)² = 841; center (-56, 8); radius 29

Solution & Explanation:Group the x-terms and y-terms, then add 784 to complete the x-square and 16 to complete the y-square. This gives (x + 28)² + (y - 4)² = 841. In standard form (x-h)²+(y-k)²=r², the center is (-28, 4) and the radius is 29.

Problem 3Difficulty: Mastery

A final answer for x² + y² - 42x + 40y - 59 = 0 must include the completed-square form, center, and radius. Which choice is correct?

ACompleted form: (x + 21)² + (y - 20)² = 900; center (-21, 20); radius 30

BCompleted form: (x - 21)² + (y + 20)² = 900; center (21, -20); radius 30

CCompleted form: (x - 21)² + (y + 20)² = 1741; center (21, -20); radius sqrt(1741)

DCompleted form: (x - 42)² + (y + 40)² = 900; center (42, -40); radius 30

Solution & Explanation:Group the x-terms and y-terms, then add 441 to complete the x-square and 400 to complete the y-square. This gives (x - 21)² + (y + 20)² = 900. In standard form (x-h)²+(y-k)²=r², the center is (21, -20) and the radius is 30.

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Frequently Asked Questions

Common questions about printing, using, and solving this worksheet

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QIs this GEO.151 Complete the square to rewrite circle equations worksheet free for teachers and homeschoolers?

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Yes! In addition to this printable worksheet, students can practice GEO.151 Complete the square to rewrite circle equations interactively on our platform with automated grading, instant score tracking, and detailed step-by-step solutions.

QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Geometry Math students. It aligns with educational standard G-GPE.A.1 (Primary standard selected for prompt fields in this prompt cell: CCSS G-GPE.A.1. Skill statement in this prompt cell: Select the correctly completed-square form of a given circle equation and identify the corresponding center and radius. Associated standards listed with this skill in the curriculum source: CCSS G-GPE.A.1; FL MA.912.GR.7.2-7.3; VA G.PC.4; TEKS §111.41(c). Use this prompt-provided wording as the supporting standard description for this workflow.).