The vertical height in feet of a projectile on a planet in our solar system at a given time t in seconds is represented by the function h(t)=−4t2+24t. Re-write h(t) in the form \large h\left(t\right)=a\left(t-h\right)^2+k and determine the maximum height of the projectile. Show all work.

Answer 1

as with all quadratics, the vertex is at t = -b/2a

Answer 2

or look for where dh/dt = 0 (stops going up, starts down)
0 = -8 t +24
t = 3 seconds
h(3)=−4*9+24 *3 = 72-36 =36 ft