Free Printable WorksheetMathAlgebra IIMath CurriculumState extension

ALG2.239 Converting Conic Equations Between Forms Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra II Math worksheet provides structured practice on ALG2.239 Converting Conic Equations Between Forms. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.239 Converting Conic Equations Between Forms - Complete the square to convert conic equations from general form to standard form and identify the conic type. (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 ALG2.239 Converting Conic Equations Between Forms skill assessments:

Problem 1Difficulty: Mastery
Which conversion is equivalent to 18x2 + 8y2 - 72x + 32y - 40 = 0?
A(x - 2)2/18 + (y + 2)2/8 = 1; ellipse
B(x - 2)2/8 + (y + 2)2/18 = 1; ellipse
C(x + 2)2/8 + (y - 2)2/18 = 1; ellipse
D(x - 2)2/8 - (y + 2)2/18 = 1; hyperbola
Solution & Explanation:Divide by 2, then complete the squares: 9(x2 - 4x) + 4(y2 + 4y) = 20. Adding 36 and 16 gives 9(x - 2)2 + 4(y + 2)2 = 72, so (x - 2)2/8 + (y + 2)2/18 = 1, an ellipse.
Problem 2Difficulty: Mastery
Without finishing every arithmetic step mentally, the opposite signs in 7x2 - 5y2 + 14x + 20y - 48 = 0 suggest a hyperbola. Which completed standard form confirms it?
A(x + 1)2/5 + (y - 2)2/7 = 1; ellipse
B(x - 1)2/5 - (y + 2)2/7 = 1; hyperbola
C(x + 1)2/5 - (y - 2)2/7 = 1; hyperbola
D(y - 2)2/7 - (x + 1)2/5 = 1; hyperbola
Solution & Explanation:Group and complete: 7(x2 + 2x) - 5(y2 - 4y) = 48. Adding the weighted constants gives 7(x + 1)2 - 5(y - 2)2 = 35. Dividing by 35 gives (x + 1)2/5 - (y - 2)2/7 = 1.
Problem 3Difficulty: Mastery
A satellite dish cross-section is represented by y2 + 4y - 20x + 44 = 0. Which standard form and type are correct?
A(y - 2)2 = 20(x + 2); parabola
B(y + 2)2 = -20(x - 2); parabola
C(x - 2)2 + (y + 2)2 = 20; circle
D(y + 2)2 = 20(x - 2); parabola
Solution & Explanation:Complete the square in y: y2 + 4y = 20x - 44. Add 4 to get (y + 2)2 = 20x - 40 = 20(x - 2), so the cross-section is a parabola.

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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: Complete the square to convert conic equations from general form to standard form and identify the conic type. 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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