Study Guide

Learning Objectives

• Write parabola equations with vertex (h, k) and correct opening (4.6.A.1).
• Write ellipse equations with center and radii; recognize circles (4.6.A.2).
• Write hyperbola equations and describe asymptotes (4.6.A.3).
• Identify and connect graphical, analytical, and verbal forms (1.B, 2.A, 2.B).

Course scope only (Unit 4 additional topic; not on the AP Exam).

Suggested Practice Sequence

1. Classify equation: one squared term (parabola), plus signs (ellipse), minus (hyperbola). 2. Read (h, k) from standard form. 3. Identify opening direction or radii a, b. 4. Plot center/vertex and a few key points. 5. Rewrite in equivalent standard form when needed (1.B).

Classroom / Check-In Moves

• "Plus or minus between squared terms?"
• "Which form: y - k = ... or x - h = ...?"
• "Is a = b? Then it's a circle."

Misconception Watch-List

• Using ellipse form for hyperbola (sign error).
• Confusing parabola axis of symmetry with hyperbola asymptotes.
• Swapping a and b on ellipse without checking denominators.
• Horizontal vs vertical parabola form reversed.

Vocabulary to Own

• vertex; center; focus (contextual)
• parabola; ellipse; hyperbola; circle
• horizontal/vertical radius; asymptote
• standard form; opening direction

Materials Map

• Practice: parabola, ellipse, hyperbola forms
• Word: satellite dishes, orbits, navigation contexts
• Mixed / multi-*: combine with 4.5 implicit and 4.7 parametric
• Review & practice test: conic fluency
• Interactive: classify and feature checks