A quadratic function is a function of the form f(x) = ax^2 + bx + c where a, b and c are constants. Part of the definition of a quadratic function is that a is not equal to zero, although b and c can equal zero.
The graph of a quadratic function, y = ax^2 + bx + c, is a parabola. This parabola has one stationary point, which is a maximum point if a is negative or a minimum point if a is positive. A quadratic function is a type of polynomial function. Quadratic functions can have one, two or no real roots.