Math Playground
Geometry

Parabola

The curve a thrown ball traces — and what every satellite dish is shaped like.

A parabola is the curve you get when you slice a cone parallel to its side. Throw a ball, watch a fountain spray, look at a satellite dish — you're seeing a parabola.

Standard form
y = a x² + b x + c

a controls how 'wide' or 'narrow' the U is.

Anatomy

  • Vertex — the tip of the curve, the highest or lowest point.
  • Axis of symmetry — vertical line through the vertex; the curve mirrors over it.
  • Focus & directrix — every point on the parabola is the same distance from the focus point as it is from the directrix line.

Parallel rays hitting a parabolic dish all bounce to the focus — that's why satellite dishes and car headlights use parabolas.