Single-shot absorption measurements have been performed using the multi-keV x rays generated by a laser-wakefield accelerator. A 200 TW laser was used to drive a laser-wakefield accelerator in a mode which produced broadband electron beams with a maximum energy above 1 GeV and a broad divergence of
≈
15
 
 
mrad
FWHM. Betatron oscillations of these electrons generated
1.2
±
0.2
×
10
6
 
 
photons
/
eV
in the 5 keV region, with a signal-to-noise ratio of approximately
300
∶
1
. This was sufficient to allow high-resolution x-ray absorption near-edge structure measurements at the
K
edge of a titanium sample in a single shot. We demonstrate that this source is capable of single-shot, simultaneous measurements of both the electron and ion distributions in matter heated to eV temperatures by comparison with density functional theory simulations. The unique combination of a high-flux, large bandwidth, few femtosecond duration x-ray pulse synchronized to a high-power laser will enable key advances in the study of ultrafast energetic processes such as electron-ion equilibration.