The equation for the axis of symmetry of a parabola in the vertex form \(y = a(x-h)^2 + k\) is given by \(x = h\), where \((h, k)\) is the vertex of the parabola.
For the given equation:
\[ y = 3(x - 1)^2 - 12 \]
Here, \(h = 1\). Therefore, the axis of symmetry is:
\[ x = 1 \]
So the final answer is:
x = 1