The equation of the axis of symmetry for a parabola in the vertex form \( y = a(x - h)^2 + k \) is given by the line \( x = h \), where \( (h, k) \) is the vertex of the parabola.
In your equation \( y = 3(x - 1)^2 - 12 \), we identify \( h \) as \( 1 \).
Therefore, the equation for the axis of symmetry is:
\[ x = 1 \]