The curve $C$ with equation $y=\frac{a x^2+b x+c}{3 x+1}$ passes through the point with coordinates $(-1,-4)$ and has a turning point at $(-3,-2)$.
(i) Find the values of $a, b$ and $c$.

[3]

(ii) Hence sketch the graph of curve $C$, stating the equations of any asymptotes and the coordinates of any points where the curve crosses the axes.

[3]