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The lesson begins with using graphs to solve quadratic inequalities. An equation modeling the height of a rocket is graphed along with a second equation that represents the minimum height at which the rocket can legally and safely be exploded. The intersections of the graphs provide the solution interval. A second method is then presented where the inequality is put into standard form and then solved for its $x$-intercepts. Interval notation and union of sets is reviewed before a purely algebraic procedure for solving the inequalities is presented. The lesson concludes with an application problem.

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