Parabolas

Math

Definition

A U-shaped curve that is the graph of a quadratic function or the set of all points equidistant from a fixed point (focus) and a fixed line (directrix). Parabolas can open up, down, left, or right.

Examples

  • The path of a thrown ball follows a parabolic arc
  • y = x² is the simplest upward-opening parabola
  • Satellite dishes use parabolic shapes to focus signals at the focus point
Key Fact

Standard forms: y = a(x-h)² + k (vertical) or x = a(y-k)² + h (horizontal); vertex at (h,k)

Related Terms

Vertex form Quadratic formula Identifying conics Ellipses

Study This Concept

Practice parabolas with free review games in these units:

Pre-Calculus Unit 8: Conic Sections