Parameters of the quasar sample. Top: luminosity functions of quasars from Quaia and the VMC survey in G band. All Quaia quasars (1.3 million objects; blue), Quaia quasars with VMC counterparts with quasar-like colors (2347 objects; orange); spectroscopically confirmed VMC quasars from this paper and from Ivanov et al. (2016) with Gaia counterparts (161 objects; red); the same as the red sample, but without the 5 objects from the bright SAAO sample and those that fall below the Quaia G=20.5 mag limit (green), projected output for a VMC survey full quasar sample (450 objects; black dots), and confirmed Quaia quasars scaled down from the full sky to the VMC survey area (~6300 objects; cyan dots), assuming a loss of 10% in the zone of avoidance. In reality, 7386 Quaia quasars fall in the VMC survey footprint, bottom: redshiſt distribution for all Quaia quasars (1.3 million objects; blue), for Quaia quasars with VMC counterparts with quasar-like colors (2347 objects; orange), and Quaia quasars with spectroscopically confirmed quasars from our VMC selection (161 objects; green). See Sect. 4 for details.