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The graph of $y=\frac{x+1}{a{{x}^{2}}+bx+c}$, where&nbsp;$a$, $b$ and $c$ are non-zero constants, has an asymptote at $x=-\frac{1}{2}$.
The graph also has a turning point at $\left( -2,\ -\frac{1}{9} \right)$.
Find the values of $a$, $b$ and $c$.[4]

The graph of $y=\frac{x+1}{a{{x}^{2}}+bx+c}$, where $a$, $b$ and $c$ are non-zero constants, has an asymptote at $x=-\frac{1}{2}$.

The graph also has a turning point at $\left( -2,\ -\frac{1}{9} \right)$.

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