Analyzing the function
[tex]f(x) = -3(x+1)^2 +12[/tex]
We can see that the "+12" at the end only causes a vertical translation, and thus won't change the axis of symmetry. So, it all comes down to find the axis of symmetry of
[tex]f(x) = -3(x+1)^2[/tex]
But again, the "-3" coefficient in front only causes the parabola to be more or less narrow, and since it's negative, it reflects it across the [tex]x[/tex] axis. So, we can focus only on the part
[tex]f(x)=(x+1)^2[/tex]
The parent function [tex]f(x)=x^2[/tex] has the line [tex]x=0[/tex] (i.e. the [tex]y[/tex] axis) as the axis of symmetry. The child function [tex]f(x)=(x+1)^2[/tex] is obtained via a transformation like [tex]f(x)\mapsto f(x+k)[/tex], which causes a horizontal translation, [tex]k[/tex] units to the left if [tex]k[/tex] is positive, [tex]k[/tex] units to the right if [tex]k[/tex] is negative. In this case, [tex]k=1[/tex], so we translate the parent function one unit to the left, and the new axis of symmetry is [tex]x=-1[/tex]
