While the high-redshift quasar luminosity function closely parallels the hierarchical growth of dark matter halos, at lower redshifts quasars exhibit an antihierarchical turnoff, which moves from the most luminous objects to the faintest. We explore the idea that this may arise from self-regulating feedback, caused by quasar outflows. Using a hybrid approach that combines a detailed hydrodynamic simulation with observationally derived relationships, we calculate the luminosity function of quasars down to a redshift of z = 1 in a large, cosmologically representative volume. Outflows are included explicitly by tracking halo mergers and driving shocks into the surrounding intergalactic medium, with an energy output equal to a fixed 5% fraction of the bolometric luminosity. Our results are in excellent agreement with measurements of the spatial distribution of quasars on both small and large scales, and we detect an intriguing excess of galaxy-quasar pairs at very short separations. Our results also reproduce an antihierarchical turnoff in the quasar luminosity function; however, this falls short of that observed, as well as that predicted by analogous semianalytic models. The difference can be traced to the treatment of gas heating within galaxies and the presence of in-shock cooling. The simulated galaxy cluster L_X-T relationship is close to that observed for z ≈ 1 clusters, but the simulated galaxy groups at z = 1 are significantly perturbed by quasar outflows. Measurements of anomalously high X-ray emission in high-redshift groups, along with detections of 1000 km s^-1 winds in poststarburst ellipticals, would provide definitive evidence for the AGN-heating hypothesis.