(a) The duty of support imposed by Section 3900 continues as to an unmarried child who has attained the age of 18 years, is a full-time high school student, and who is not self-supporting, until the time the child completes the 12th grade or attains the age of 19 years, whichever occurs first.
(b) Nothing in this section limits a parent’s ability to agree to provide additional support or the court’s power to inquire whether an agreement to provide additional support has been made.