Answer: The correct option is (D) (-2, -7).
Step-by-step explanation: We are given to identify the vertex for the graph of the following function :
\(y=3x^2+12x+5~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\)
We know that
the vertex of the graph of the function \(y=a f(x-h)+k\) is given by \((h,k).\)
From equation (i), we have
\(y=3x^2+12x+5\\\\\Rightarrow y=3(x^2+4x)+5\\\\\Rightarrow y=3(x^2+4x+4)+5-12\\\\\Rightarrow y=3(x+2)^2-7\\\\\Rightarrow y=3\{x-(-2)\}^2+(-7).\)
Therefore, the vertex of the graph of function (i) will be
\((h,k)=(-2,-7).\)
Thus, (D) is the correct option.
