Can quarter horse thoroughbred registered

Answer 1

A thoroughbred/quarter horse X is called an apendix. They cannot race on the track, but there is an apendix registry. I wouldn't say that all apendixes show the good qualities of both breeds; on the contrary, I think that many show off all of the bad traits.

Answer 2

Appendix Quarter horses can definitely race. An appendix quarter horse mare must be bred to a quarter horse (permanent registry) stallion with the resulting foal registered as a quarter horse. Appendix horses that compete and reach a certain level of accomplishment can be advanced into the permanent registry at the discretion of the registry. For racing appendix horses this is a speed index of 80 or greater.
The AQHA is replete with Thoroughbred stallions like Three Bars, Azure Te, Nolhome, Top Deck, Beduino and more recent TB stallions like Favorite Trick and Hennesey.