This document discusses two methods for solving quadratic inequalities: graphing and using a sign diagram. For graphing, the inequality is graphed like a boundary line and the range where the inequality is true is shaded. For the sign diagram method, the zeros of the quadratic function are placed on a number line and the intervals where the function has the same sign as the inequality are determined to be the solution set. Examples of both methods are shown and key aspects like critical numbers and sign changes are explained.