Answer: \(x\)-intercepts \((-2,0)\), \((1,0)\), \((3,0)\); \(y\)-intercept \((0,18)\).

The key point is to identify the important features of the graph before using it to answer the question.

The \(x\)-intercepts occur when any factor is zero:

\(x-3=0,\qquad x-1=0,\qquad x+2=0.\)

So the graph cuts the \(x\)-axis at

\((3,0),\quad(1,0),\quad(-2,0).\)

The \(y\)-intercept is found by putting \(x=0\):

\(y=3(-3)(-1)(2)=18.\)

So the graph cuts the \(y\)-axis at

\((0,18).\)

The cubic has positive leading coefficient, so its left-hand end goes downwards and its right-hand end goes upwards. It crosses the \(x\)-axis at \(-2\), \(1\) and \(3\).