Let $f(x)=\sqrt{a{x}^2+bx}$. For how many real values of $a$ is there at least one positive value of $b$ for which the maximum value of $f$ is equal to the length of its domain? (If the domain is an infinite interval, its length is considered $\infty$. If the maximum value of $f$ is $\infty$, then it is considered equal to the length.)