The killing of Jonathan M. Levin, a son of the Time Warner chairman, by one of his former high school students in 1997 transfixed a city that was breaking free of its crime-ridden past.

Five years later, the New York City Education Department opened Jonathan Levin High School for Media and Communications in the same South Bronx building where he had taught, declaring it “a living tribute” to the English teacher’s “spirit, values, commitment and impassioned belief” that every child has a right to a quality education.

But in the past few years, a quality education at Levin High School became harder to come by. Money for a college scholarship in Mr. Levin’s name dried up. A ball field that a Mets official helped pay for fell into disrepair. Computers sat untouched, applications to the school fell and the graduation rate sank to 31 percent, the fifth-lowest in the city.

Now, just a decade after it opened, New York has deemed Levin High School a failure, and is preparing to close it down.