Question

An archer shoots an arrow into the air such tht its height at any time, t, is given by the function h(t) = -16t² + kt + 3. If the maximum height of the arrow occurs at time t = 4, what is the value of k?

Answer 1

h'(t) = 0 gives you maximum height,
so assuming k is a constant,
h'(t)=-32t+k
0=-32t+k
if t=4 then k= 32*4
k=128

Double check,
h(t)=-16t^2+ 128t+ 3
h'(t)=-32t+128
h'(t)=0=-32t+128
128/32 = t
4=t.

There you go.

Answer 2

you can also just find the x coordinate of the vertex which is
-k/(-2*16) =4 k/32=4 4X32

Since it is a parabola the maximum height will occur at the vertex

Answer 3

thanks you