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)=−6t2+24t . Re-write h(t) in the form h(t)=a(t-h)^2+k and determine the maximum height of the projectile. Show all work.

Question

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)=−6t2+24t  . Re-write h(t) in the form h(t)=a(t-h)^2+k and determine the maximum height of the projectile. Show all work.
Can someone help me? Please and thank you.

oobleck · Answer

-6t^2+24t = -6(t^2-4t) = -6(t^2+4t+4) +6(4) = -6(t-2)^2 + 24 the vertex is at t=2, and h(2) = 24