I wouldn't ever buy a car without running a carfax on it first. Of course, if you like the car, take it to a certified mechanic and have it checked out. If the mechanic likes it, ask him how much HE would pay for the car. Then make your offer based on the mechanic's input. Never buy a car with that many miles on it without having it checked out first. Ask questions about the transmission, engine and other mechanical stuff, like the front-end alignments, etc. I always ask when the last time the car was aligned. If it never was, I walk away. Proper alignments save many things, like tires and wear and tear on critical steering parts.
In any case, $2400 for a car that is going to drop out of the NADA book this quarter is not a bargain. Offer $1200 and walk away if you don't get the car.