The Staging Platform for a Fireworks Display Is 8 Ft $h ( t ) = - 16 ( t - 5 ) ^ { 2 } + 408$

Essay

The staging platform for a fireworks display is 8 ft above ground, and the mortars leave the platform at 160 ft/sec. The height of the mortars h(t) (in feet) can be modeled by $h ( t ) = - 16 ( t - 5 ) ^ { 2 } + 408$ where t is the time in seconds after launch.
a. If the fuses are set for 5 sec after launch, at what height will the fireworks explode?
b. Will the fireworks explode at their maximum height? Explain