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H(t)= -5t^2 + at + b
At time t=0, a ball was thrown upward from the top of a building. Before the ball hit the ground, its height h(t), in feet,
at the time t seconds is given by the function above. A and b are constants.
If the ball reached its maximum height of 125 feet at time t=3, what could be the height of the building?
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Before starting my solution, I must make this notice.
The form of your equation (the coefficient -5 at t^2) means that the units are (should be/must be) METERS, not feet.
So, I will solve it assuming that the input is in METERS.
Solution
The fact that "the ball reached its maximum height of 125 feet at time t=3" means that the vertex form of the quadratic function H(t) is
H(t) = .
It means that H(t) = = = .
In turn, it means that the height of the building is 80 meters.
Answer. The height of the building is 80 meters.