  We present a combined analysis of the applications of the weighted horizontal
magnetic gradient (denoted as WG_M in Korsos et al., ApJ, 802, L21, 2015)
method and the magnetic helicity tool (Berger & Field, JFM, 147, 133, 1984)
employed for three active regions (ARs), namely NOAA AR11261, AR11283 and
AR11429. All three active regions produced series flares and CMEs. We followed
the evolution of the components of the WG_M and the magnetic helicity before
the flare and CME occurrences. We found an unique and mutually shared behavior,
called the U-shaped pattern, of the weighted distance component of WG_M and of
the shearing component of the helicity flux before the flare and CME eruptions.
This common pattern is associated with the decreasing-receding phase yet
reported only known to be a necessary feature prior to solar flare eruption(s),
but found now at the same time in the evolution of the shearing helicity
parameter. This result leads to the conclusion that (i) the shearing motion of
photospheric magnetic field may be a key driver for the solar eruption in
addition to the flux emerging process, and that (ii) the found
decreasing-approaching pattern in the evolution of shearing helicity may be
another precursor indicator for improving the forecasting of solar eruptions.
