Exploring Quadratic Functions

Quadratic functions form parabolas and have an axis of symmetry. They can be written in standard form as ax^2 + bx + c = y, where a cannot equal 0. The vertex of the parabola occurs at the minimum if a > 0 and it opens upwards, or at the maximum if a < 0 and it opens downwards. Quadratic functions can be graphed using a table of values in a graphing calculator or by hand. Ordering quadratic functions from widest to narrowest depends on the coefficient a, with larger absolute values of a producing narrower parabolas.