The given function is:
[tex]f(x)=3x^2+6x-2[/tex]Complete the square and factor as follows:
[tex]\begin{gathered} f(x)=3(x^2+2x+1)-2-3 \\ f(x)=3(x+1)^2-5_{} \end{gathered}[/tex]Compare with:
[tex]f(x)=a(x-h)^2+k[/tex]To get:
[tex](h,k)=(-1,-5)[/tex]Since the parabola is vertical the axis of symmtery is vertical which is x=-1.