Quadratic relations are mathematical expressions that describe a specific type of relationship between variables, typically represented in the form of a quadratic equation, such as y = ax² + bx + c. In this equation, a, b, and c are constants, and x is the variable. The graph of a quadratic relation is a curve called a parabola, which can open upwards or downwards depending on the value of a. These relations are commonly found in various real-world situations, such as projectile motion, where the path of an object follows a parabolic trajectory. Quadratic relations can also be used in areas like economics, physics, and engineering to model relationships that involve squared terms, making them essential in both theoretical and applied mathematics.