Question 1088880
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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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<U>Before starting my solution, I must make this notice</U>.


<pre>
    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.
</pre>

<U>Solution</U>


<pre> 
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) = {{{-5(t-3)^2 + 125}}}.


It means that H(t) = {{{-5t^2 + 30t + (-5*9) + 125}}} = {{{-5t^2 + 30t -45 + 125}}} = {{{-5t^2 + 30t + 80}}}. 


In turn, it means that the height of the building is 80 meters.
</pre>

<U>Answer</U>.  The height of the building is 80 meters.