Final answer:
The height of the stone at the initial time t = 0 is given by substituting t = 0 into the quadratic equation, resulting in 32 feet.
Step-by-step explanation:
The question involves determining the height of an object at a specific point in time, given its initial conditions - a stone thrown upward from the top of a building, described by the quadratic function h(t) = -16t2 + 64t + 32. To find the height after t seconds, we substitute t with the desired time value into the function.
At t = 0, the height is the initial height from which the stone is thrown. As we substitute t = 0 into h(t), we get h(0) = -16(0)2 + 64(0) + 32= 32 feet.
Therefore, the stone starts 32 feet above the ground, which matches option a) 32 feet. This height is the initial value of the stone's position before it begins its upward trajectory.