4. Let the function be
$$
f(x)=a x^{2}+4 x+b \text{, }
$$

the equation $f(x)=x$ has two real roots $\beta_{1}$ and $\beta_{2}$. If $a$ and $b$ are both negative integers, and $\left|\beta_{1}-\beta_{2}\right|=1$, then the coordinates of the vertex of the graph of the function $f(x)$ are $\qquad$