Properties of Quadratic Functions

1.  Quadratic Functions have the form y(x) = a x^2 + b x + c.

2.  The graph of a quadratic function is a parabola.

3.  The parabola is symmetric about its vertical axis of symmetry.

4.  The vertex is the extreme point of the parabola and lies on the axis of symmetry.

5.  The zeros of the function lie at x = (-b +- sqrt(b^2 - 4 a c) ) / (2a).

6.  The axis of symmetry of the function is the line x = - b / (2 a), which lies halfway between the zeros as long as the function has real zeros.