[tex]Plug \ in \ x+3 \ into \ f(x) \ to \ get \ g(x)
\\\ g(x) = (x+3)^2-2(x+3)+6
\\\ g(x)= x^2+6x+9 -2x-6+6
\\\ g(x) = x^2+4x+9
\\\ -\frac{b}{2a} --\ \textgreater \ vertex
\\\ \frac {-4}{2}
\\\ x \ coordinate = -2, plug \ it \ back \ into \ g(x)
\\\ (-2)^2+4(-2)+9
\\\ 4-8 + 9
\\\ y \ coordinate = 5
\\\ \boxed{(-2,5)}[/tex]
