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)