Parabola

Parabola

A u-shaped curve with certain specific properties. Formally, a parabola is defined as follows: For a given point, called the focus, and a given line not through the focus, called the directrix, a parabola is the locus of points such that the distance to the focus equals the distance to the directrix.

Note: It is a common error to call any u-shaped curve a parabola. A parabola must satisfy the conditions listed above, and a parabola always has a quadratic equation.

Two parabola graphs: vertical (vertex (h,k), y=a(x-h)²+k) and horizontal (vertex (h,k), x=a(y-k)²+h), with orientation notes...

Diagram of a parabola with vertex (h,k), focus point p above vertex. Formulas: vertical 4p(y-k)=(x-h)², horizontal 4p(x-h)=(y-k)².

Parabola diagram showing point P on curve, focus inside curve, directrix below. L1 (to focus) = L2 (to directrix).

Example:

Graph of upward-opening parabola with vertex at (3,-2), focus above vertex, vertical axis of symmetry at x=3, and horizontal...

This is a graph of the parabola with all its major features labeled: axis of symmetry, focus, vertex, and directrix.