A quadratic function is a polynomial function of the form f(x)=ax^2+bx+c, where a cannot equal 0. It is a second degree polynomial with the highest exponent being 2. Setting a quadratic function equal to 0 produces a quadratic equation, whose solutions are the roots of the equation. Quadratic functions are commonly used to model real world phenomena like projectile motion or profit functions and appear in nature as parabolic shapes.