If you have plead guilty by paying the fine on the speeding ticket then the conviction for the violation will be placed on your driving record at this point in most all states. If points are to be assessed to your license they would also be done so at this point in time. You can check with your state's Department of Motor Vehicles to find out the number of points or if your state assigns points for moving violations.

When your parents inform their insurance company that you are licensed and want to place you on their insurance, the insurance provider will usually pull your motor vehicle record (MVR) and thus see the speeding ticket. If the ticket is not yet on your driving record but there is an application for insurance that requests information on your driving record such as if you have any tickets you would need to list or disclose this ticket.

Depending upon the insurance companies rating system this may affect the rates you receive and your parent's total premium. Your parents should be able to find out about their insurance carrier's rating system for moving violations by asking their agent.