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if a projectile is fired straight upward from the ground with an initial speed of 32 feet per second, then its height h in feet after t seconds is given by the function h(t)= -16t^2 + 160t. Find the maximum height of the projectile?

400 ft

Step-by-step explanation:

h(t)= -16t^2 + 160t

The vertex is found at

h = -b/2a  where b is the coefficient of t and a is the coefficient of t^2

   = -160/(2*-16)

   -160/-32

  5

The time where the maximum occurs is at t=5

To find the maximum substitute into the function

h(5) = -16 (5)^2 +160*5

       = -16*25 +800

       =-400+800

       = 400

The maximum height is 400 ft