Focus of a Parabola – Vertex, Focus, Directrix Practice

Focus of a Parabola – Vertex, Focus, Directrix Practice | Algebra 2 Worksheet

This in-depth Algebra 2 worksheet gives students the structured practice they need to understand and apply the geometric definition of a parabola using the vertex, focus, directrix, and axis of symmetry. Perfect for classwork, homework, sub plans, or review, this resource is aligned to Common Core Standard HSF.IF.C.7.A and provides a mix of skill-building and real-world application.

What’s Included:

• Warm-Up Section
  • Definitions and key vocabulary: parabola, vertex, focus, directrix, axis of symmetry
  • Review of graphing quadratic functions and completing the square
• Part A: Pre-requisite Review
  • 2 essential skill problems on graphing and rewriting quadratics in vertex form
• Part B: Convert to Vertex Form + Identify Focus & Directrix (10 problems)
  • Students rewrite quadratics and calculate the focus, directrix, and axis of symmetry
• Part C: Write Equations from a Given Vertex and Focus (10 problems)
  • Practice deriving equations of parabolas that open up, down, left, or right
• Part D: Graph from a Given Focus and Directrix (10 problems)
  • Students sketch parabolas, label all key features, and write the matching equation

• Part E: Real-World Applications (10 problems)
  • Word problems including satellite dishes, flashlight reflectors, bridges, and more

• Part F: Challenge Problems (10 problems)
  • Includes derivations, transformations, and advanced concept applications

• Complete Answer Key
  • All 60+ problems are fully solved for easy grading or student self-check

Additional Features:

• 100% Editable in Word or Google Docs – easy to adapt for your specific classroom needs
• Designed to cover 90–120 minutes of instruction and practice
• Can be used digitally or printed for in-class or homework use
• Great for differentiation, reteaching, or enrichment

Standards Alignment:

• CCSS: HSF.IF.C.7.A – Graph linear and quadratic functions and show intercepts, maxima, and minima

Ideal for:

• Algebra 2 full-lesson practice
• Pre-AP/Advanced Algebra students
• Homework packets or intervention
• Substitute plans
• Concept mastery and review before assessments

Terms of Use: This resource is licensed for use by one teacher in one classroom. Please do not share, distribute, or post this resource online. If another teacher would like to use it, please direct them to purchase their own copy. Thank you for supporting Minute Math!