Familial Potions Prompting Fatherhood

Harry purposefully destroyed his potion to reveal your parents. Snape calls him back for a detention to rebrew it. Is it possible that Harry is able to correctly brew a potion without the help of a certain book. (NO SLUGHORN) Mentions of abuse,rape, self harm and suicide. Severitus. I don't own these awesome characters. Snape is Harry's dad. Continued if requested...