A quadratic function is a type of mathematical function that can be expressed in the standard form f(x) = ax^2 + bx + c , where a , b , and c are constants, and a ≠ 0 . The graph of a quadratic function is a parabola, which can open either upward or downward depending on the sign of a . Quadratic functions are commonly used in various fields, including physics and engineering, to model situations such as projectile motion. The solutions to a quadratic function can be found using the quadratic formula, which is x = \frac-b \pm \sqrt{b^2 - 4ac}2a .