The information on the symmetry energy and its density dependence is deduced by comparing the available data on the electric dipole polarizability αD of 68Ni, 120Sn, and 208Pb with the predictions of the random-phase approximation, using a representative set of nuclear energy density functionals. The calculated values of αD are used to validate different correlations involving αD, the symmetry energy at the saturation density J , the corresponding slope parameter L, and the neutron skin thickness rnp, as suggested by the droplet model. A subset of models that reproduce simultaneously the measured polarizabilities in 68Ni, 120Sn, and 208Pb are employed to predict the values of the symmetry energy parameters at saturation density and rnp. The resulting intervals are J =30-35 MeV, L=20-66 MeV; and the values for rnp in 68Ni, 120Sn, and 208Pb are in the ranges 0.15-0.19, 0.12-0.16, and 0.13-0.19 fm, respectively. The strong correlation between the electric dipole polarizabilities of two nuclei is instrumental to predict the values of electric dipole polarizabilities in other nuclei.