Here is a question from an IB past paper -

> 
> The function $f$ is such that $f(x)=a^{2}x^{2}-ax+3b\;$ for
>  $\;\displaystyle x\leq\frac{1}{2a},\;$ where $a$ and $b$ are constants. 
> 
> 
> For the case where $f(-2)=4a^{2}-b+8\;$ and $f(-3)=7a^{2}-b+14,\;$
>  find the possible values of $a$ and $b$.
> 
> 
> 

I'm not sure how to go about solving this.

My working so far -

Since $\displaystyle x\leq\frac{1}{2a},$

$\Rightarrow\;\displaystyle -2\leq\frac{1}{2a}$

$\therefore\;\displaystyle a\leq-\frac{1}{4}$

$\Rightarrow\;\displaystyle -3\leq\frac{1}{2a}$

$\therefore\;\displaystyle a\leq-\frac{1}{6}$