  We show that the Hilbert-Kunz density function of a quadric hypersurface of
Krull dimension $n+1$ is a piecewise polynomial on a subset of $[0, n]$, whose
complement in $[0, n]$ has measure zero. Our explicit description of the
Hilbert-Kunz density function confirms a conjecture of Watanabe-Yoshida on the
lower bound of the Hilbert-Kunz multiplicity of the quadric of dimension $n+1$,
provided the characteristic is at least $n-1$. We also show that the
Hilbert-Kunz multiplicity of a quadric of fixed dimension is an eventually
strictly decreasing function of the characteristic confirming a conjecture of
Yoshida.
  The main input comes from the classification of Arithmetically Cohen-Macaulay
bundles on the projective variety defined by the quadric via matrix
factorizations.
