We have studied the high magnetic field (less than or equal to 50 T) dependence of the negatively charged exciton properties in GaAs/AlxGa1-xAs (x = 0.33) quantum wells using photoluminescence (PL) spectroscopy. Observation of all the optically allowed transitions of the charged exciton allows us to experimentally verify a revised energy-level diagram of spin-split singlet and triplet states. The PL data obtained on all samples are completely consistent with this diagram, leading us to conclude that the negatively charged exciton is a model three-particle system. The binding energy of the negatively charged exciton is measured between 23 and 50 T, and found to be constant for both singlet and triplet states. Our results are compared with recent theory.