On top of a hill, a rocket is launched from a distance 80 feet above a lake. the rocket will fall into the lake after its engine burns out. the rocket's height, h, in feet above the surface of the lake, is given by the equation, h = -16t 2 + 64t + 80, where t is time in seconds. the maximum height of the rocket is 144 a0 feet.

For this case we have the following equation:
 h = -16t2 + 64t + 80
 To find the maximum height, we derive the equation:
 h = -32t + 64
 We match zero:
 -32t + 64 = 0
 We clear t:
 t = 64/32
 t = 2
 We substitute the value of t in the given equation:
 h (2) = -16 * (2) ^ 2 + 64 * (2) + 80
 h (2) = 144
 
 The maximum height is 144 feet and the time to reach this height is 2 seconds.

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