Please help!

h(t)    =-3t^2  + 12t + 60

Let h(t)  = y

We want the form

y  = a (x - h)^2  + k      where k  will give us the max  height

Factor out the  -3

y  = -3 (t^2 - 4t - 20)          take 1/2 of 4  = 2...square it = 4 ...  add and subtract this within the parentheses

y = -3 ( t^2  - 4t + 4  - 20  - 4)  simplify within the parenthese

y = -3 (t^2 - 4t + 4   - 24)      factor the first three terms

y = -3 [ (t - 2)^2  - 24 ]     distribute the "-3"  across the terms in the bracket

y = -3 (t - 2)^2  + 72

k = 72  =  max ht  (in feet)