We present a measurement of the time-dependent CP-violating asymmetries in neutral B decays to the eigenstate, and an updated measurement of the charge asymmetry in B0→K+π-~ decays. In a sample of 33 million Y(4S)→BB̄ decays collected with the BABAR detector at the SLAC PEP-II asymmetric B factory, we find 65-11+12 and 217±18 K+π- candidates and measure the asymmetry parameters Sππ=0.03-0.56+0.53±0.111, Cππ=-0.25-0.17+0.45±0.14, and AKπ = -0.07±0. 08±0.02, where the first error is statistical and the second is systematic. © 2002 The American Physical Society.