  We investigate a second order $parabolic$ parametrization,
$w(a)=w_t+w_a(a_t-a)^2$, 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 DR11 and improved WiggleZ. We found the existence of a turning
point in $w$ at $a\sim0.7$ is favored at 1$\sigma$ CL. In the epoch $0.55< a<
0.9$, $w<-1$ is favored at 1$\sigma$ CL, and this significance increases near
$a=0.8$, reaching a 2$\sigma$ CL. The parabolic parametrization achieve
equivalent performance to the $\Lambda$CDM 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 $w$.
