We consider negabent Boolean functions that have Trace representation. We
completely characterize quadratic negabent monomial functions. We show the
relation between negabent functions and bent functions via a quadratic
function. Using this characterization, we give infinite classes of
bent-negabent Boolean functions over the finite field $\F_{2^n}$, with the
maximum possible degree, $n \over 2$. These are the first ever constructions of
negabent functions with trace representation that have optimal degree