  Here we prove that the Hilbert-Kunz mulitiplicity of a quadric hypersurface
of dimension $d$ and odd characteristic $p\geq 2d-4$ is bounded below by
$1+m_d$, where $m_d$ is the $d^{th}$ coefficient in the expansion of
$\mbox{sec}+\mbox{tan}$. This proves a part of the long standing conjecture of
Watanabe-Yoshida. We also give an upper bound on the HK multiplicity of such a
hypersurface.
  We approach the question using the HK density function and the classification
of ACM bundles on the smooth quadrics via matrix factorizations.
