Parabola The purpose of this discussion is to: find an equation to a real-life situation such as the problem described below. Suppose the staging platform for a fireworks display is 6 ft above ground, and the mortars leave the platform at  96 ft/sec. The height of mortars h(t) (in feet) can be modelled by, h(x) = -16t^2 + 96t + 6 where t is the time  in seconds after launch: Find the following 1.  If the fuses are set for 3 sec after launch, at what height will the fireworks explode? 2.  Will the fireworks explode at their maximum height? Explain Instruction:  Discuss the fact why it is a parabola problem. Set up an equation of the form:  h(x) = a(t-h)^2 + k Use the vertex formula to write the equation and solve the problem above.

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.