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