The Parabola (mathematics)

A parabola is a U-shaped curve described mathematically by a quadratic equation, typically y = ax² + bx + c. It is symmetric around a central axis called the axis of symmetry, and its vertex is the highest or lowest point on the curve. Parabolas naturally occur in physics, such as the trajectory of a projectile under gravity, and in engineering, like satellite dishes and car headlights, because they can focus signals or forces effectively. The shape results from the geometric definition of a parabola as the set of points equidistant from a fixed point (focus) and a fixed line (directrix).