We first complete the square.
y=-x^2+2x+1
y=-x^2+2x-1+1+1
y=-(x-1)^2+2
The maximum point is (1,2) since -1 in ( ) meant 1 unit to the right and +2 meant 2 units up.
The maximum point is (1,2) but the maximum value means the y value which is simply just 2.
Done!