An archer shoots an arrow into the air such that its height at any time, t, is given by the function h(t) = -16t^2 + kt + 3. If the maximum height of the arrow occurs at time t = 4, what is the value of k?
(1) 128 (3) 8
(2) 64 (4) 4
All right. In that case we need to look at the height function a bit more carefully. It is an inverted parabola. The maximum height will be at the vertex of the parabola, which is on the axis of symmetry.
Given a parabola the axis of symmetry will be the line .
We have the parabola . We know that the location of the max height is the line t = 4, which is our axis of symmetry. So:
So
.
-Dan