parabola

The curve given by a quadratic equation `y = ax² + bx + c` (with `a ≠ 0`), or — equivalently — the set of points equidistant from a fixed point (focus) and a fixed line (directrix). It appears whenever a quantity changes as the _square_ of another quantity: in projectile motion as the trace of constant horizontal velocity meeting constant vertical acceleration, in optics as the cross-section that focuses parallel light to a single point, in basic algebra as the graph of any quadratic function. A parabola is the _image_; many different motions can paint it.