The diagram shows the graph of \(y=\mathrm{f}(x)=x^3+ax^2+bx+c,\ x\in\mathbb R\), where \(a,\ b,\) and \(c\) are real constants. The graph cuts the \(x\)-axis at the points \((-1,0),\ (1,0)\) and \((2,0)\).
Find the value of \(a\), of \(b\), and of \(c\).[3]
The graph of \(y=\mathrm{f}(x)\) is translated by \(\begin{pmatrix}m\\0\end{pmatrix}\) to the graph of \(y=\mathrm{g}(x)\) such that the \(y\)-intercept of \(y=\mathrm{g}(x)\) is also its minimum turning point. Find the value of \(m\).[2]
Using the value of \(m\) to 3 significant figures, sketch the graph of \(y=\mathrm{g}(-|x|)\), labelling its \(x\)-intercepts.[4]