Which case approved the school's right to suspend or discipline a student who uses profane or obscene language or gestures?

The case is Bethel School District vs Freser ( 1986 ).

This was a landmark decision made by the Supreme Court involving free speech in public schools. Matthew Fraser, a high school student, was suspended from school in the Bethel School District in Washington because of a speech he made at a school assembly.

The Supreme Court held that his suspension did not violate the First Amendment.

Matthew Fraser made a speech nominating a fellow student for an elective office. There, he used a graphic sexual metaphor to promote his friend's candidacy. The Bethel High School used its disciplinary code to enforce a rule that prohibits conduct which ' substantially interferes with the education process ... including the use of obscene, profane language or gestures'.

Matthew Fraser was suspended from school for three days.

well considering i can't see the graph, it's probably prices