Free Printable WorksheetMathPre-CalculusMath CurriculumCCSS HSG-GPE.A.1-3(+)

Pre CAL.116 Determine Focus, Directrix, and Latus Rectum for Parabolas Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Pre-Calculus Math worksheet provides structured practice on Pre CAL.116 Determine Focus, Directrix, and Latus Rectum for Parabolas. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.116 Determine Focus, Directrix, and Latus Rectum for Parabolas - Primary standard selected for prompt fields in this prompt cell: CCSS HSG-GPE.A.1-3(+). Skill statement in this prompt cell: Given a parabola equation, determine the focus and directrix and select the correct sketch showing these features. Associated standards listed with this skill in this prompt cell: CCSS HSG-GPE.A.1-3(+); CCSS HS-Modeling; SMP 1,2,4,5,7,8; AP Precalculus CED Units 3-4; TX §111.42(c)(3)(D-H); FL MA.912.GR.7.1-7.9, MA.912.T.4.5-4.7; VA MA.AG.1-2. 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

Pre-Calculus

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 Pre CAL.116 Determine Focus, Directrix, and Latus Rectum for Parabolas skill assessments:

Problem 1Difficulty: Mastery
Use the four labeled sketch options to match the parabola 10(y - 2)2 = -5(x + 5) with its focus and directrix.
ASketch A
BSketch B
CSketch C
DSketch D
Solution & Explanation:Divide by 10 to get (y - 2)2 = (-1/2)(x + 5). For (y - k)2 = 4p(x - h), 4p = -1/2, so p = -1/8. The focus is (h + p, k) = (-41/8, 2) and the directrix is x = h - p = -39/8.
Problem 2Difficulty: Mastery
For the parabola 12(x + 4)2 = 3(y - 1), select the sketch that correctly shows the vertex, focus, and directrix.
ASketch A
BSketch B
CSketch C
DSketch D
Solution & Explanation:Divide by 12 to get (x + 4)2 = (1/4)(y - 1). For (x - h)2 = 4p(y - k), 4p = 1/4, so p = 1/16. The focus is (h, k + p) = (-4, 17/16) and the directrix is y = k - p = 15/16.
Problem 3Difficulty: Mastery
For the parabola x = -0.125(y - 3)2 + 2, which option gives the focus, directrix, and latus rectum length?
AFocus (4, 3); directrix x = 0; latus rectum length 8
BFocus (-6, 3); directrix x = 10; latus rectum length 32
CFocus (3/2, 3); directrix x = 5/2; latus rectum length 2
DFocus (0, 3); directrix x = 4; latus rectum length 8
Solution & Explanation:Since -0.125 = -1/8, rewrite the vertex form as (y - 3)2 = -8(x - 2). For (y - k)2 = 4p(x - h), 4p = -8, so p = -2. The focus is (h + p, k) = (0, 3) and the directrix is x = h - p = 4. The latus rectum length is |4p| = 8.

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Pre-Calculus Math students. It aligns with educational standard CCSS HSG-GPE.A.1-3(+) (Primary standard selected for prompt fields in this prompt cell: CCSS HSG-GPE.A.1-3(+). Skill statement in this prompt cell: Given a parabola equation, determine the focus and directrix and select the correct sketch showing these features. Associated standards listed with this skill in this prompt cell: CCSS HSG-GPE.A.1-3(+); CCSS HS-Modeling; SMP 1,2,4,5,7,8; AP Precalculus CED Units 3-4; TX §111.42(c)(3)(D-H); FL MA.912.GR.7.1-7.9, MA.912.T.4.5-4.7; VA MA.AG.1-2. Use this prompt-provided wording as the supporting standard description for this workflow.).

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