A parabola is a symmetrical, U-shaped curve that can be defined mathematically as the set of all points equidistant from a fixed point, called the focus, and a fixed line, known as the directrix. Parabolas are commonly found in various real-world applications, such as satellite dishes and car headlights, where they help focus light or signals. In a coordinate system, a parabola can be represented by a quadratic equation, typically in the form of y = ax² + bx + c. The value of a determines the direction and width of the parabola, while the vertex is the highest or lowest point on the curve, depending on its orientation.