<p>
bvg1100 - I came back to the forum a few days ago after a long break, so I missed your question.</p>
<p>f(x) = a (x - h) ^2 + k<br>
is the vertex form of a parabolas equation;
(h, k) is the vertex.</p>
<p>Rewriting the given equation
h(t) = c - (d - 4t )^2 in the vertex form:
h(t) = -(d 4t)^2 + c
h(t) = -(4 (d/4 t) )^2 + c
h(t) = -((4)^2) (d/4 t)^2 + c
h(t) = -16 (t - d/4)^2 + c;
(d/4, c) is the vertex.</p>
<p>The ball reaches the maximum height h = 106 at t = 2.5:
(2,5; 106) is the vertex.
(d/4, c) = (2,5; 106)
d/4 = 2.5
d = 10 and c = 106.</p>
<p>Back to the given equation
h(t) = c - (d - 4t )^2:<br>
h(t) = 106 - (10 4t)^2.</p>
<p>The height of the ball at the time t = 1
h(t) = 106 - (10 4(1))^2 = 106 6^2 = 70 feet.</p>