a) To find the height of the flare 2 seconds after it was shot, we can substitute t=2 into the function h(t):
h(2) = -16(2)² + 90(2) = -64 + 180 = 116
Therefore, the height of the flare 2 seconds after it was shot is 116 feet.
b) To express the function in factored form, we can factor out -16t from the right side:
h(t) = -16t(t - 5.625)
Therefore, the function in factored form is h(t) = -16t(t - 5.625).
c) To evaluate h(2) using the factored form from part b), we can substitute t=2 into the factored form:
h(2) = -16(2)(2 - 5.625) = -16(-3.625) = 58
Therefore, h(2) = 58 when using the factored form of the function.