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

Pre CAL.106 Derive and Interpret Parabola Equations 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.106 Derive and Interpret Parabola Equations. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.106 Derive and Interpret Parabola Equations - 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 or key features, determine vertex, focus, directrix, and opening direction and select the matching graph. 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.106 Derive and Interpret Parabola Equations skill assessments:

Problem 1Difficulty: Mastery
A parabola has focus (2, -6) and directrix y = 4. Which set of features and equation are correct?
AVertex (2, -1); p = -5; (x - 2)2 = -20(y + 1); opens down
BVertex (2, -1); p = 5; (x - 2)2 = 20(y + 1); opens up
CVertex (-1, 2); p = -5; (y - 2)2 = -20(x + 1); opens left
DVertex (2, 4); p = -10; (x - 2)2 = -40(y - 4); opens down
Solution & Explanation:The vertex is halfway between y = -6 and y = 4, so it is (2, -1). The focus is 5 units below the vertex, so p = -5 and the equation is (x - 2)2 = -20(y + 1), opening down.
Problem 2Difficulty: Mastery
Evaluate this statement: For any vertical parabola (x - h)2 = 4p(y - k), if p < 0, the directrix lies above the vertex. Which choice is correct?
ATrue; y = k - p is greater than k when p is negative
BFalse; y = k - p is less than k when p is negative
CFalse; the directrix is x = h - p for every vertical parabola
DFalse; p changes the width but never the directrix position
Solution & Explanation:The directrix is y = k - p. If p is negative, subtracting p adds a positive amount to k, so the directrix is above the vertex.
Problem 3Difficulty: Mastery
Which statement correctly compares x2 = 12y and y2 = 12x?
Ax2 = 12y opens up with focus (0, 3), while y2 = 12x opens right with focus (3, 0).
BBoth open up because 12 is positive.
Cx2 = 12y opens right with focus (3, 0), while y2 = 12x opens up with focus (0, 3).
DBoth have the same directrix y = -3.
Solution & Explanation:For both equations, 4p = 12 so p = 3. The equation x2 = 12y is vertical and opens up with focus (0, 3); y2 = 12x is horizontal and opens right with focus (3, 0).

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Frequently Asked Questions

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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 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 or key features, determine vertex, focus, directrix, and opening direction and select the matching graph. 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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