h= -16t^2 + 32t + 9
The t coordinate of the vertex is given by : - 32 / 2(-16) = -32 / -32 = 1
And to find the h coordinate, just put the t coordinate into the function :
-16(1)^2 + 32(1) + 9 = -16 + 32 + 9 = 16 + 9 = 25
So....the vertex is (t, h) = (1, 25)