A car can't curve on a slippery plane road (with zero friction). So clearly, what plays as the centripetal force that makes the car able to curve in friction, which is exerted by the road surface to the four tires of the car. You also learned that when curving, the car's tire are rotating (not slipping) so the friction is static friction.
Why can a car slip when moving too fast on a curving horizontal road? This is because the speed of the car exceeds the allowed limit to make the turn. The formula for the speed limit or maximum limit that is allowed to make a safe turn on a rough horizontal curving road can be derived as follows. The source of centripetal force is friction fs so:
Fs = fs ----> Fs = μsN = μsmg
by definition, the formula for centripetal force is
Fμs = mv2max /r
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