Answer: \(f(x)=-\frac12(x+2)(x+1)(x-5)\), and \(-2\leq x\leq-1\) or \(x\geq5\).

(a) From the graph, the roots are

\(x=-2,\qquad x=-1,\qquad x=5.\)

So

\(f(x)=a(x+2)(x+1)(x-5).\)

The graph crosses the \(y\)-axis at \(5\), so \(f(0)=5\). Hence

\(5=a(2)(1)(-5)=-10a.\)

Therefore

\(a=-\frac12.\)

So

\(f(x)=-\frac12(x+2)(x+1)(x-5).\)

(b) The graph is on or below the \(x\)-axis between the first two roots and to the right of the last root.

Therefore

\(-2\leq x\leq-1\quad\text{or}\quad x\geq5.\)