Free Printable WorksheetMathAlgebra IIMath CurriculumState extension

ALG2.234 Conic Sections Parabolas and Circles (State Extension) Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra II Math worksheet provides structured practice on ALG2.234 Conic Sections Parabolas and Circles (State Extension). Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.234 Conic Sections: Parabolas and Circles (State Extension) - Select the equation, inequality, expression, or function that represents and graph equations of parabolas and circles, identify vertex or center, focus or radius, and convert between general and standard forms by completing the square. (State extension; uses CCSS A-SSE.3b techniques.)

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 ALG2.234 Conic Sections Parabolas and Circles (State Extension) skill assessments:

Problem 1Difficulty: Mastery
Completing the square for x2 + y2 - 10x + 14y + 65 = 0 gives (x - 5)2 + (y + 7)2 = 9, so the circle has radius 3.
ATrue
BFalse
Solution & Explanation:The completed form is (x - 5)2 + (y + 7)2 - 9 = 0, or (x - 5)2 + (y + 7)2 = 9. Since r2 = 9, the radius is 3.
Problem 2Difficulty: Mastery
A graph shows a circle whose diameter endpoints are (-6, 1) and (2, 1). Which equation matches the graph?
A(x + 2)2 + (y - 1)2 = 16
B(x - 2)2 + (y + 1)2 = 16
C(x + 2)2 + (y - 1)2 = 64
D(x - 2)2 + (y + 1)2 = 64
Solution & Explanation:The midpoint of the diameter is (-2, 1), and the diameter length is 8, so the radius is 4. Therefore the equation is (x + 2)2 + (y - 1)2 = 16.
Problem 3Difficulty: Mastery
The focus of the parabola (x - 3)2 = -16(y + 2) is used as the center of a circle with radius 6. Which equation represents the circle?
A(x - 3)2 + (y + 2)2 = 36
B(x + 3)2 + (y - 6)2 = 36
C(x - 3)2 + (y - 6)2 = 36
D(x - 3)2 + (y + 6)2 = 36
Solution & Explanation:The parabola has vertex (3, -2) and 4p = -16, so p = -4. The focus is (3, -6). A circle centered there with radius 6 is (x - 3)2 + (y + 6)2 = 36.

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Frequently Asked Questions

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QHow do I download and print this ALG2.234 Conic Sections Parabolas and Circles (State Extension) worksheet?

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QIs this ALG2.234 Conic Sections Parabolas and Circles (State Extension) worksheet free for teachers and homeschoolers?

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QCan students practice ALG2.234 Conic Sections Parabolas and Circles (State Extension) online with instant feedback?

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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 State extension (Primary standard selected for prompt fields in this prompt cell: Not listed in source (State extension). Skill statement in this prompt cell: Select the equation, inequality, expression, or function that represents and graph equations of parabolas and circles, identify vertex or center, focus or radius, and convert between general and standard forms by completing the square. Associated standards listed with this skill in the curriculum source: State extension; uses CCSS A-SSE.3b techniques. Use this prompt-provided wording as the supporting standard description for this workflow.).

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