  In this paper, we will interest in finding the number of zeros of the
quadratic forms over finite fields. We will apply the tool for finding the
number of rational points of supersingular curves in [6]. We will give some
more tools for Artin-Schreier curves related with quadratic form. We will
especially interest in the (supersingular) Artin-Schreier curve
$y^q-y=x^{q^b+1}-x^{q^a+1}$.
