If the files are .jp2 (JPEG2000) the georeferencing is built in. Otherwise, you will need the .jgw or.jpgw (World File) for QGIS to understand the georeferencing. If you do not have the World File the .jpg image will be dumb. Do you still have access to ArcGIS, as you may be able to either create the World File or save as .jp2? If you have an ArcGIS .aux.xml file associated with the image, this may have the georeferencing information, in which case you could construct a World File. I am not sure if QGIS understands.aux.xml files.