Question 55110
determine vertex of y=x^2-8x+22 
You are almost on the right track.
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 y=x^2-8x+22 
x^2-8x+? = y-22+?
x^2-8x+16 = y-22+16
(x-4)^2 = y-6
This follows the form (x-h)^2=4p(y-k)
where (h,k) is the vertex.
Vertex is (4,6)
Cheers,
Stan H.