[en] Using data collected by the high-energy photoproduction experiment FOCUS at Fermilab we performed a Dalitz plot analysis of the Cabibbo favored decay D⁺→K^-π⁺π⁺. This study uses 53653 Dalitz-plot events with a signal fraction of ∼97%, and represents the highest statistics, most complete Dalitz plot analysis for this channel. Results are presented and discussed using two different formalisms. The first is a simple sum of Breit-Wigner functions with freely fitted masses and widths. It is the model traditionally adopted and serves as comparison with the already published analyses. The second uses a K-matrix approach for the dominant S-wave, in which the parameters are fixed by first fitting Kπ scattering data and continued to threshold by Chiral Perturbation Theory. We show that the Dalitz plot distribution for this decay is consistent with the assumption of two-body dominance of the final state interactions and the description of these interactions is in agreement with other data on the Kπ final state