The equation of the axis of symmetry for 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.
In the given equation \(y = 3(x-1)^2 - 12\), we can identify \(h\) and \(k\):
- \(h = 1\)
- \(k = -12\)
Thus, the equation for the axis of symmetry is:
\[ x = 1 \]