Answer :
The Solution.
The given parabola is
[tex]y=3x^2+12x+11[/tex]Let the vertex of the given parabola be (h,k).
So,
[tex]\begin{gathered} h=-\frac{b}{2a} \\ \text{Where a=3,b=12,c=11} \end{gathered}[/tex]Substituting these values, we get
[tex]h=-\frac{12}{2\times3}=-\frac{12}{6}=-2[/tex]Now, substituting -2 for x in the given parabola, we get
[tex]\begin{gathered} k=3(-2)^2+12(-2)+11 \\ k=3(4)-24+11 \\ k=12-24+11 \\ k=-12+11=-1 \end{gathered}[/tex]So, the vertex of the given parabola is (-2,-1)
Thus, the correct answer is option B.