The parents face multiple charges including causing or allowing the death of a child, causing or allowing serious physical harm, sexual assault and cruelty. The mother also faces a charge of murder. Both defendants deny the charges.
The child and her parents are not being named to protect her identity.
Opening the prosecution case, counsel told the jury the child had suffered a skull fracture, a subdural haemorrhage in her brain, fractured ribs, a broken right arm, multiple bruises and a burn covering her entire face.
The prosecution said the injuries had occurred on different occasions over at least five weeks before her death, culminating in fatal head injuries.
The mother was allegedly the only adult present when the fatal injuries were inflicted. Prosecutors said medical evidence indicated a forceful impact against a hard surface and severe shaking.
The court heard that the child had previously been taken into care and later returned to her parents. Prosecutors questioned whether the prospect of housing assistance had influenced their decision to care for her rather than proceed with adoption.
The prosecution alleged that the mother recorded videos showing her daughter lifeless and with a significant facial burn before calling emergency services, and that medical help had not been sought for the burn. Police attempted to save the child, who was later pronounced dead at hospital.
Prosecutors also alleged that the child had suffered sexual abuse.
The court heard that the father was living elsewhere under bail conditions following an arrest for allegedly assaulting the mother. Prosecutors said he had nevertheless seen his daughter and that her facial burn would have been highly visible.
The prosecution also described searches by the mother concerning mental health, burns and imprisonment for beating a child.
The trial continues.