The graph of $y=f(x)$ is shown in the $xy$-plane. The function $f$ is defined by $f(x)=a{x}^2+bx+c$, where $a,b,$ and $c$ are constants. The graph is a parabola opening upwards, with its vertex at $(0,-3)$. It passes through the points $(-2,1)$ and $(2,1)$.

For how many values of $x$ does $f(x)=1$?