I'm taking an introductory analysis course and I can't seem to get this. Here is the definition for continuity at a point:

$f:A\rightarrow B$ is continuous at $c\in A$ iff:

$\forall \epsilon>0$, $\exists \delta>0$ such that $|x - c|<\delta$ (and $x\in A)$ $\Rightarrow |f(x) - f(c)| <\epsilon$. 

Here is my work thus far:

Note $f(c)=f(2)=3$.

I work backwards from $|f(x) - f(c)| <\epsilon$:

$|f(x) - f(c)| = |2x^2 - 3x + 1 - 3| = |2x^2 -3x-2|=|(2x+1)(x-2)|$

I notice that $|x-2|$ is $|x-c|$ as $c=2$. Seems... convenient. Not sure where to go from here though, how can I get rid of that $(2x+1)$ term?