Buying a vehicle with an extensive ownership and trade-in history is not advisable. Such a vehicle becomes a liability to the buyer; there is a reason the vehicle continues to switch hands and owners. Utah license plate history will reveal the number and type of previous owners (whether they were individuals, businesses using the vehicle for livery, or law enforcement).
Make sure there are no liens on the car. If there is a lien, this means the bank technically owns the car, and it cannot be transferred to you legally until the entire loan is paid in full. You want to confirm the seller is the current owner and that the title is clean and legal, ready for transfer of ownership to you.