What is the axis of symmetry of f(x) = -3(x+1)to the power of 2 +12

Analyzing the function

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

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 axis. So, we can focus only on the part

The parent function has the line (i.e. the axis) as the axis of symmetry. The child function is obtained via a transformation like , which causes a horizontal translation, units to the left if is positive, units to the right if is negative. In this case, , so we translate the parent function one unit to the left, and the new axis of symmetry is