He faces up to life in prison when he is sentenced July 2.
During a preliminary hearing in 2nd District Court, a medical examiner said the infant died as a result of shaking and trauma to her head.
According to court records, the child was brought to a local hospital on Dec. 14, 2011, and died later that day. An autopsy concluded that the child suffered from a lethal closed head injury.
"Marshall stated that while he was attending to [the child] in the middle of the night that he forcefully put K.M. back in her crib, hitting her head pretty had on the crib," plea agreement documents filed court state. "Mr. Marshall later admitted to his mother in a conversation regarding what happened with K.M. that he 'murdered somebody.' "
The child's mother, Afton Moneypenny, told the Salt Lake Tribune in 2012 that Marshall was good with the child, but that doctors later found cracked ribs and other injuries.
"He's put his hands on me before," Moneypenny said. "But I didn't think he had the capacity of killing someone, especially a baby."