Answer: \(a=1\), with \(b=2,c=-1\) or \(b=-1,c=2\). For \(y\geqslant2\), approximately \(-1.7\leqslant x\leqslant-1\) or \(x\geqslant1.2\).

From the graph, the three \(x\)-intercepts are approximately

\(x=-2,\quad x=-\frac12,\quad x=1.\)

The factor \(2x+a\) gives the root \(x=-\frac{a}{2}\). Since one root is \(-\frac12\),

\(a=1.\)

The other two roots are produced by \(x+b\) and \(x+c\). Thus \(b\) and \(c\) are \(2\) and \(-1\), in either order.

To solve \(y\geqslant2\), read from the graph where the curve is on or above the horizontal line \(y=2\). The intersections with \(y=2\) are approximately

\(x=-1.7,\quad x=-1,\quad x=1.2.\)

Therefore

\(-1.7\leqslant x\leqslant-1\quad\text{or}\quad x\geqslant1.2.\)