the number of solutions of an equation in Galois field

Question

Let $f$ be an odd prime power and consider the Galois field of order $f$, $GF\left(f\right)$. Consider the equation $z^{2}=y^{k}+a_{1}y^{k-1}+a_{2}y^{k-2}+...+a_{k-1}y+a_{k}$, where $\lbrace z,y,a_{1},...,a_{k} \rbrace$ are elements of $GF\left(f\right)$. what is the number of solutions $(z,y)$, $z\neq 0$, that satisfy in this equation?