we know that
The equation of the vertical parabola is of the form
[tex]y=a(x-h)^{2} +k[/tex]
where
[tex](h,k)[/tex] is the vertex of the parabola
In this problem we have
[tex]g(x)=3(x-2)^{2} -5[/tex]
The parabola open upward
The vertex is a minimum
The vertex is the point [tex](2,-5)[/tex]
therefore
the answer is the option C
[tex](2,-5)[/tex]
