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.