4. If the quadratic function $f(x)=a x^{2}+b x+c$ has a line of symmetry at $x=1$, and its graph passes through the point $(2,0)$, then the value of $\frac{f(-1)}{f(1)}$ is ( ).
(A) -3
(B) -2
(C) 2
(D) 3
4. A.

From the problem, we know the curve passes through the point $(0,0)$, so $c=f(0)=0$.
Thus, $f(x)=a x^{2}+b x$.
Also, the axis of symmetry of the graph is $x=\frac{-b}{2 a}=1$, i.e., $b=$ $-2 a$, then $\frac{f(-1)}{f(1)}=\frac{a-b}{a+b}=-3$.