Consider the equation $y^2 = f(x)$, in the finite field $\mathbb{F}_q$($q$ is a prime power) where $f(\cdot)$ is a monic polynoimal of even degree (greater than or equal to $4$) with integer coefficients. Let $N_f$ be the number of solutions of the above equation in the finite field $\mathbb{F}_q$.
Is it true that $|N_f - q| \le C_f \sqrt{q}$, for some constant $C_f$?