The high school cheerleader relegated to the JV squad for another year responded with a fleeting fit of frustration: a photo of her upraised middle finger and another word that begins with F.

“F--- school, f--- softball, f--- cheer, f--- everything,” 14-year-old Brandi Levy typed into Snapchat one spring Saturday. Like all “snaps” posted to a Snapchat “story,” this one sent to about 250 “friends” was to disappear within 24 hours, before everyone returned to Pennsylvania’s Mahanoy Area High School on Monday.

Instead, an adolescent outburst and the adult reaction to it has arrived at the Supreme Court, where it could determine how the First Amendment’s protection of free speech applies to the off-campus activities of the nation’s 50 million public school students.

“This is the most momentous case in more than five decades involving student speech,” said Justin Driver, a Yale law professor and author of “The Schoolhouse Gate: Public Education, the Supreme Court, and the Battle for the American Mind.”