The body of Leonne Weeks was found in Dinnington, Rotherham, on Monday at about 11:00 GMT.
An 18-year-old man is being quizzed over her murder and a woman, 26, is being held on suspicion of assisting an offender.
Her family said they were "devastated at the loss of our beautiful daughter and sister Leonne".
"She was very much loved and will be missed by all of us," they added.
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Rebecca Staples, principal of Dinnington High School, of which Leonne was a pupil, said the community was "reeling".
"We have extra security at school at the moment because we wanted to be sure ourselves and want parents to be sure that everyone is absolutely safe," she added.
"I think there's also a feeling of underlying anger that something like this could have happened in such a close community to one of our own.
"She was a lovely student, a lively student and it's a sad loss."
A post-mortem examination took place on Wednesday and found she had suffered multiple stab wounds, South Yorkshire Police said.
Temporary Det Ch Insp Martin Tate added: "Leonne's family have had their entire lives turned upside down over the last couple of days and are utterly devastated."
Police have been granted an extension to the murder suspect's custody as they continue with inquiries.
Friends and family posted Facebook appeals for Leonne's whereabouts on Monday morning after she failed to return home.
By 18:00, comments hoping she would be found safe had changed to well wishes to the family after "heartbreaking news".
Patrols have been increased in the area to reassure the community and anyone with information is urged to make contact.
A 16-year-old girl found on a path had been stabbed to death, police said.