The shape of the hadronic form factor f(+)(q(2)) in the decay D-0 -> K(-)e(+)nu(e) has been measured in a model independent analysis and compared with theoretical calculations. We use 75 fb(-1) of data recorded by the BABAR detector at the PEP-II electron-positron collider. The corresponding decay branching fraction, relative to the decay D-0 -> K-pi(+), has also been measured to be R-D=B(D-0 -> K(-)e(+)nu(e)(gamma))/B(D-0 -> K-pi(+)(gamma))=0.927 +/- 0.007 +/- 0.012. From these results, and using the present world average value for B(D-0 -> K-pi(+)), the normalization of the form factor at q(2)=0 is determined to be f(+)(0)=0.727 +/- 0.007 +/- 0.005 +/- 0.007 where the uncertainties are statistical, systematic, and from external inputs, respectively.