Definition 1

The graph of y = x² is called a parabola. The point (0, 0) is called the vertex of the parabola and the y axis is the axis of symmetry of the parabola called simply the axis.

Some other parabolas are the graphs of y = ax² + bx + c where a ≠ 0.

More generally, every parabola is similar to the graph of y = x².

Definition 2

A parabola is the locus of all points P such that the distance from P to a fixed point F is equal to the distance from P to a fixed line l.