  Quadratic algebras of the type $\lsb Q_0, Q_\pm \rsb$ $=$ $\pm Q_\pm$, $\lsb
Q_+, Q_- \rsb$ $=$ $aQ_0^2 + bQ_0 + c$ are studied using three-mode bosonic
realizations. Matrix representations and single variable differential operator
realizations are obtained. Examples of physical relevance of such algebras are
given.
