Answer: \(x\)-intercepts \(-4,-\frac12,3\); \(y\)-intercept \(3\).

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

The \(x\)-intercepts occur when

\(-\frac14(2x+1)(x-3)(x+4)=0.\)

Therefore

\(2x+1=0,\quad x-3=0,\quad x+4=0.\)

So the \(x\)-intercepts are

\(x=-\frac12,\quad x=3,\quad x=-4.\)

For the \(y\)-intercept, put \(x=0\):

\(y=-\frac14(1)(-3)(4)=3.\)

So the \(y\)-intercept is \(3\). The coefficient of \(x^3\) is negative, so the cubic rises to the left and falls to the right.