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Richard Parker was the father of Peter Parker. He and his wife Mary left when Peter was young, for unknown reasons.

Biography

To be added

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In the comics, Richard Parker along with his wife Mary Parker were CIA agents, but when things went bad for the CIA they became S.H.I.E.L.D. agents. Richard and Mary Parker were later killed by the third Red Skull, Albert Malik. It is highly doubtful this will happen in the film as Sony holds the rights to Spider-Man and Marvel Studios owns the rights to S.H.I.E.L.D. and Red Skull.
In the Ultimate Comics Universe, Richard and Mary were scientists working at Trask Industries until they died in a plane crash orchestrated by the mysterious benefactor of Richard's Venom project (heavily implied to be Oscorp) when Richard refused to give up the suit (which was a bodysuit rather than symbiote in this continuity). In the the trailer, Peter finds a device similar to what he would use as his webshooters, and Ben attributes it to Richard, therefore implying this incarnation of the character is also a scientist.