Answer: The height above the ground in feet of a football thrown into the air from the balcony of a house is given by the expression:
h(t) = -12t^2 + 20t + 30
where t is the time in seconds since the ball was thrown.
To find the height of the balcony above the ground, we need to determine the initial height of the football when it was thrown from the balcony. This initial height corresponds to the value of h(0), since the time elapsed since the throw was zero at that moment.
Therefore, we can substitute t = 0 into the expression for h(t):
h(0) = -12(0)^2 + 20(0) + 30 = 30
This means that the balcony is 30 feet above the ground.
Hence, the height of the balcony above the ground is 30 feet.
Explanation: