The maximum height occurs at the vertex found using t = -b/2a
The time = t=-20/2*-5 = -20/-10 = 2 seconds.
Now replace t with 2 in the equation to solve for the height:
h(t) = -5t^2 +20t +1
h(2) = -5(2)^2 +20(2) +1
h(2) = -5(4) + 40 + 1
h(2) = -20 + 41
h(2) = 21 meters.
Maximum height was 21 meters at 2 seconds.