we have the equation
y=x^2-6x+2
this equation represents a vertical parabola open upward (because the leading coefficient is positive)
that means
the vertex is a minimum
Convert to vertex form
y=a(x-h)^2+k
where
(h,k) is the vertex
Complete the square
y=(x^2-6x+9)+2-9
y=(x-3)^2-7
therefore
the vertex is (3,-7)
