Question
The height above the ground in feet of a ball kicked into the air from the balcony of an apartment is: -16t^2 + 16t + 32, where t is the time in seconds since the ball was kicked. How high above the ground is the balcony?
Answers
GPT-4o mini
To find the height above the ground of the balcony from which the ball was kicked, we evaluate the height function at \( t = 0 \). The height function is given by:
\[
h(t) = -16t^2 + 16t + 32
\]
Substituting \( t = 0 \):
\[
h(0) = -16(0)^2 + 16(0) + 32
\]
This simplifies to:
\[
h(0) = 0 + 0 + 32 = 32
\]
Thus, the height above the ground of the balcony is \( \boxed{32} \) feet.
\[
h(t) = -16t^2 + 16t + 32
\]
Substituting \( t = 0 \):
\[
h(0) = -16(0)^2 + 16(0) + 32
\]
This simplifies to:
\[
h(0) = 0 + 0 + 32 = 32
\]
Thus, the height above the ground of the balcony is \( \boxed{32} \) feet.