The energy and parity eigenstates for quadrupolar, triple [delta]-function potential are analysed. Using the analytical solutions in specific domains, simple expressions are obtained for even- and odd-parity bound-state energies. The Heisenberg uncertainty product is observed to have a minimum for a specific strength of the potential. The scattering states have a transmission resonance for some energies, and the poles of the transmission coefficients correspond to bound-state energies. These features are of considerable pedagogical interest in the understanding of quantum-mechanical properties of bound and scattering states, for graduate and general physicists. (Contains 2 tables and 3 figures.)