We use the Risaliti & Lusso (2015) compilation of 808 X-ray and UV flux measurements of quasars (QSOs) in the redshift range \(0.061 \leq z \leq 6.28\), alone and in conjuction with baryon acoustic oscillation (BAO) and Hubble parameter [\(H(z)\)] measurements, to constrain cosmological parameters in six cosmological models. The QSO data constraints are significantly weaker than, but consistent with, those from the \(H(z)\) + BAO data. A joint analysis of the QSO + \(H(z)\) + BAO data is consistent with the current standard model, spatially-flat \(\Lambda\)CDM, but mildly favors closed spatial hypersurfaces and dynamical dark energy.