h=-16(t-2)^2+141

Question

The function h=-16(t-2)^2+141 gives the height in feet of an object thrown from a building where is time since the object was thrown (in seconds). After how many seconds does the object reach its maximum height? What is the maximum height?

Answer 1

vertex is (2, 141) = maximum of 141 feet in 2 seconds

the parabola's equation is in vertex form

h(t) = -16(x-2)^2 + 144

h(t) = -16(x-h)^2 +k where (h,k) = (2,144)= the vertex = maximum, with k=144 = maximum height, and h=2 seconds = time when max is reached

or expand the function

h(t) = -16(x^2-4x +4) + 144 = -16t^2 +64x -64 +144

= -16t^2 +64x + 80

take the derivative and set equal to zero

h'(t) =-32t +64 = 0

t = 64/32 = 2 seconds to reach max height

h(2) = max height = -16(2)^2 +64(2) + 80

= -16(4) + 128+80

= -64 +128+80

= 64+80 = 144 = maximum height