Yousef Makki, 17, who dreamed of becoming a heart surgeon, was stabbed on Saturday evening in Hale Barns, a leafy village south of Manchester popular with top footballers and celebrities.
Two boys, also aged 17, are in custody on suspicion of murder. On Monday evening, a Greater Manchester Police spokeswoman confirmed detectives had been granted another 24 hours to question the pair.
The victim, from Burnage, Manchester, is thought to have won a scholarship to attend the £12,000 a year independent Manchester Grammar School.
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In a tribute, his family said: "Yousef was a loving and caring son and brother, and he meant the world to his family.
"He was a sporty young man, a dedicated student and so bright. He had everything to look forward to.
"We are absolutely devastated and cannot believe that our son has gone. This senseless loss has affected the whole community.
"Yousef had only phoned home hours earlier to say that he would be home for his tea, but the next knock at the door were officers with the tragic news, it is every parent's worst nightmare.
"We would appeal to anyone with information to contact the police and to help us find out what has happened on Saturday evening.
"Only recently had we talked about his promising life ahead of him and how he was looking forward to life. He was a promising student and loved by everyone."
Police were first alerted around 6:40pm on Saturday to reports a teenager had been stabbed on Gorse Bank Road, Hale Barns.
Officers attended the scene and Yousef was taken to hospital where he died a short time later.
Floral tributes have been left on the tree-lined street where Yousef was found injured.
A two-minutes silence was held on Monday by pupils and staff at his school, which described him as a "a dearly loved young man and incredibly bright pupil" who was studying four A-levels and had aspirations to pursue a career in medicine.
The High Master, Dr Martin Boulton, said: "It is impossible to make sense of such a senseless act, which has taken away a proud family's son, a dear friend and a young man of such promise.
"There has been an outpouring of grief at School at this tragic loss.
"The thoughts of the whole school community are with Yousef's family.
"At this time, we would ask that the privacy of his family and friends is respected, while we all mourn and seek to come to terms with what has happened."
Leading the murder investigation, Detective Chief Inspector Colin Larkin, of Greater Manchester Police, said: "The last couple of days have been absolutely devastating for Yousef's family - something no mother or father should ever have to live through.
"Our specialist officers have been supporting them as we continue our investigation but now I turn to the community for their help.
"Do you have any information that could help us with our enquiries? Do you know something but you've not yet made contact with us?
"We know there were vehicles in the area around the time of the fateful incident, did you see something? Please send us your dashcam footage and any information you have as soon as possible.
"Don't do it for me, do it for his family who tonight, and every night from now on, will have to go to sleep knowing they'll never see Yousef again."
Anybody with information should contact police on 0161 856 6777 or the independent charity Crimestoppers, anonymously, on 0800 555 111.
Dashcam footage can be sent directly to [email protected]