Veritas 2008-2009 monitoring of the variable gamma-ray source m 87

M 87 is a nearby radio galaxy that is detected at energies ranging from radio to very high energy (VHE) gamma rays. Its proximity and its jet, misaligned from our line of sight, enable detailed morphological studies and extensive modeling at radio, optical, and X-ray energies. Flaring activity was observed at all energies, and multi-wavelength correlations would help clarify the origin of the VHE emission. In this paper, we describe a detailed temporal and spectral analysis of the VERITAS VHE gamma-ray observations of M 87 in 2008 and 2009. In the 2008 observing season, VERITAS detected an excess with a statistical significance of 7.2 standard deviations (sigma) from M 87 during a joint multi-wavelength monitoring campaign conducted by three major VHE experiments along with the Chandra X-ray Observatory. In 2008 February, VERITAS observed a VHE flare from M 87 occurring over a 4 day timespan. The peak nightly flux above 250 GeV was (1.14 +/- 0.26) x 10(-11) cm(-2) s(-1), which corresponded to 7.7% of the Crab Nebula flux. M 87 was marginally detected before this 4 day flare period, and was not detected afterward. Spectral analysis of the VERITAS observations showed no significant change in the photon index between the flare and pre-flare states. Shortly after the VHE flare seen by VERITAS, the Chandra X-ray Observatory detected the flux from the core of M 87 at a historical maximum, while the flux from the nearby knot HST-1 remained quiescent. Acciari et al. presented the 2008 contemporaneous VHE gamma-ray, Chandra X-ray, and Very Long Baseline Array radio observations which suggest the core as the most likely source of VHE emission, in contrast to the 2005 VHE flare that was simultaneous with an X-ray flare in the HST-1 knot. In 2009, VERITAS continued its monitoring of M 87 and marginally detected a 4.2 sigma excess corresponding to a flux of similar to 1% of the Crab Nebula. No VHE flaring activity was observed in 2009