The Height in Feet of a Projectile with an Initial $h ( t ) = - 16 t ^ { 2 } + 128 t + 50.$

Multiple Choice

The height in feet of a projectile with an initial velocity of 128 feet per second and an initial height of 50 feet is a function of time t, in seconds, given by $h ( t ) = - 16 t ^ { 2 } + 128 t + 50.$ Find the maximum height of the projectile.

A) 409 ft
B) 306 ft
C) 404 ft
D) 162 ft
E) 498 ft