To find the vertex, you need to find the axis of symmetry first.
In order to find the axis of symmetry we have to do -b/2a.
In our case, the b is -8 and the a is 1.
Plug it in.
-(-8)/2(1)
8/2 = 4
Our axis of symmetry is 4.
Now, we plug it into the equation to find the rest of the vertex.
y = 4^2 - 8(4) + 1
y = 16 - 32 + 1
y = -16 + 1
y = -15
Put it together.
Our vertex is (4,-15).