There are a few ways to do it. Here's how I would get it. Take the derivative and set it to zero and solve for x. That gives the x coordinate of the vertex. Then plug that x value in the function to see which y value corresponds. The derivative is given by
y'=2x-8
So set it to zero and get x
2x-8=0
2x=8
x=4
Now put x=4 in your original function
4^2-8(4)+2=-14
So the vertex is at (4, -14)
