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.

The bank announced the closures as part of a "strategic review".
It said the move was a result of falling customer demand, and because of overlaps with other nearby branches.
Seven are in Aberdeen and the north east, four in Tayside, and three in the Highlands. Two are in Edinburgh, two in central Scotland, two in west Scotland and one in Lothian, Glasgow and Forth.
The full list is:
A Bank of Scotland spokesperson said: "In 2014 Lloyds Banking Group announced a three-year strategy, which included a programme of planned branch closures.
"As part of this strategic review, we can confirm today that Bank of Scotland will be closing 23 branches.
"In most cases, this is as a result of falling customer demand while in others it is because of overlaps with other nearby branches.
"Branches will continue to play an important role in our multi-channel customer offering.
"Bank of Scotland is committed to maintaining a local presence and we expect to continue to have the largest branch network in Scotland."

And former Kilmarnock boss Kenny Shiels has told BBC Scotland he would be "very interested" in the role.
Ian Baraclough parted company with the club on Wednesday, a day after the Steelmen had been knocked out of the Scottish League Cup by Greenock Morton.
Former Well captain and current Under-20s coach Stephen Craigan has been put in caretaker charge of the first team.
His first assignment will be at home to Partick Thistle on Saturday.
Shiels, most recently of Thai side BEC Tero Sasana, was considered by Motherwell last year but ultimately missed out as Baraclough was appointed in December.
And, when asked on Radio Scotland's Sportsound about the current vacancy, Shiels said: "I'm very interested because I see it as a good fit for me.
"It's a provincial club and I've had a period now where I've worked in a [Scottish FA] youth academy in Scotland and I can see so much good going on down there with [academy director] Scott Leitch at Motherwell's academy,
"There is a good conveyor belt coming through and I see massive potential at that club, I really do."
The Northern Irishman, who won the Scottish League Cup with Killie in 2012, also indicated he would be willing to work with Motherwell's current coaching staff.
After leaving Killie in 2013, Shiels had a short spell in charge of Morton before his role with the SFA and subsequent move to Thailand. He has also managed several clubs in his homeland.
"One of my greatest skills is the management of the staff and certainly that would be one that I would welcome," he added. "Stephen's a good lad."
A 16-year-old girl found on a path had been stabbed to death, police said.
[NEXT_CONCEPT]
The Bank of Scotland has announced it is to close 23 branches in Scotland.
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Motherwell have received more than 30 applications for the vacant manager's position at Fir Park.