Rahees Mahmood was the passenger on the quad driven by a 19-year-old man who was also seriously injured in the incident.
Their quad was struck by a silver Ford Focus on Broadstone Way in Holme Wood just after 4pm on Thursday.
The collision was initially treated as intentional and two men aged 19 and 30 were arrested on suspicion of murder. They have since been released under investigation.
However a man and a woman have now been arrested and are currently being held in custody.
Mr Mahmood, who lived locally, suffered serious head injuries and died at the scene. The driver remains in hospital in a serious but stable condition.
Enquiries remain ongoing and police are urging anyone with any information to come forward and assist with the investigation.
Contact West Yorkshire Police's Homicide and Major Enquiry Team via 101 quoting crime reference 13210276071.
Information, CCTV and video images which could assist enquiries can also be uploaded to our Major Incident Public Portal for Operation Parryfield at https://mipp.police.uk/operation/13XM020121B28-PO1