A parabola is a symmetrical, U-shaped curve that can open either upward or downward. It is defined as the set of all points that are equidistant from a fixed point called the focus and a fixed line known as the directrix. Parabolas are commonly found in mathematics, physics, and engineering, particularly in the study of quadratic functions. In a coordinate system, the standard form of a parabola's equation is y = ax^2 + bx + c, where a, b, and c are constants. The value of a determines the direction and width of the parabola. Parabolas also have important applications, such as in the design of satellite dishes and the trajectory of projectiles.