We investigate a second order parabolic parametrization, w（a） = wt ＋ wa（at - a）2, which is a direct characterization of a possible turning in w. The cosmological consequence of this parametrization is explored by using the observational data of the SNLS3 type Ia supernovae sample, the CMB measurements from WMAP9 and Planck, the Hubble parameter measurement from HST, and the baryon acoustic oscillation （BAO） measurements from 6dFGS, BOSS DRI 1 and improved WiggleZ. We found the existence of a turning point in w at a - 0.7 is favored at 10- CL. In the epoch 0.55 〈 a 〈 0.9, w 〈 -1 is favored at 10- CL, and this significance increases near a - 0.8, reaching a 20- CL. The parabolic parametrization achieve equivalent performance to the ACDM and Chevallier-Polarski-Linder （CPL） models when the Akaike information criterion was used to assess them. Our analysis shows the value of considering high order parametrizations when studying the cosmological constraints on w.
