First, I recommend that you read the criteria for graduation. There may be some provisions for graduation without passing the "Regents' Exam". The laws vary and it is difficult to answer your question without more information about your location and your child's educational program.
Contact your administrator or school counselor to inquire about what requirements need to be met for your child to continue beyond high school.
I will assume you are discussing the New York Regent's examinations. There are now levels of graduation criteria established in the state of New York, some which include non-regents options. Your guidance office should be able to answer any of these questions.