Search for TeV emission from a flux-limited sample of blazars with VERITAS

High-frequency-peaked BL Lacs (HBLs) dominate the extragalactic TeV sky, with more than 50 objects detected by the current generation of ground-based TeV gamma-ray observatories. In the last two years, the VERITAS telescope array has observed a flux-limited sample of 36 X-ray selected HBLs with the goal of producing the first unbiased census of TeV emission from HBL blazars. The VERITAS HBL sample contains known TeV sources as well as 15 objects for which TeV emission has not been detected before. We will present preliminary results of these VERITAS observations as well as a path to use this program to derive the luminosity function of TeV-emitting blazars. We will also discuss VERITAS observations of the blazar H 1426+428 in 2021 when it was observed to undergo a months-long high TeV flux state. The constraints that these observations place on gamma-ray emitting region of this blazar will be presented.