Parker was described Friday as "a wonderful mom and a good person" by neighbor and friend Shelly Lems.
"AJ and her daughter touched our hearts. ... She was very sincere and down to earth," Lems said. "She had just found heaven on earth here in Central and was excited about life. We will miss AJ and her daughter ..."
Authorities have said Parker and Jorgensen were in a relationship and had been living together at 176 E. Valley View Road, where the shootings occurred, since May 2011.
Eliza attended Enterprise Elementary School. The Washington County School District sent a team of counselors to the school Friday to speak to students and staff, said Tammy Davies, a secretary with the district.
Jorgensen who graduated from Pine View High School in St. George has no criminal convictions in Utah according to a court records search.
Friends of the man said they were baffled by news of the killings.
Ken Nelson, a firearm training colleague and friend of Jorgensen for the past 2½ years, said the news of his death came "totally out of the blue." He said he last saw Jorgensen three weeks ago while teaching a training event. Jorgensen brought his girlfriend whom he said he had been dating for about three months and her daughter to show them where he spent all his time.
Jorgensen worked for a soft drink bottling company, but volunteered as an instructor and president of the rifle range at the Southern Utah Shooting Sports Park. Nelson said "his passion was shooting and training people [to shoot]." So he got certified and began building a rifle-training business and a website.
"This is why it is so surprising," Nelson said. "He was doing things."
Nelson said at the time of the shooting Jorgensen was in the middle of doing his three-week block training courses, building a clientele base and planning courses out for 2013.
Recently, Jorgensen told Nelson that he was happy with how things were going with his girlfriend, and that things were becoming more serious. There was nothing to indicate the couple didn't get along, Nelson said, although he could tell they were "new" in the relationship.
Nelson added that Jorgensen was someone who kept his cool and never got angry, even out on the range.
"He was very calm and very soft-spoken," Nelson said. "No one, at least in our circles, pegged him as being capable of [murder-suicide]."
In a profile on his blog, http://gunsfreedompolitics.blogspot.com, Jorgensen said he was a Marine veteran and was "medically discharged for my back issues."
"My passion is to teach people the correct way to use firearms so that they can be both safe and fun," he wrote. "My goal in life is to own a gun store with shooting range attached."
Nelson said Jorgensen served four years in the U.S. Marine Corps infantry, and before being discharged spent a couple of years training in small-arms tactics and also trained response teams for nuclear emergencies, but he never served overseas.
Washington County Sheriff Cory Pulsipher has said he was unaware of any prior police calls to the home on Valley View Road.
Pulsipher said a family member found the shooting victims inside the single-story ranch-style residence. Property records indicate Parker's family also lives in Central.
The town of 613 residents is a mix of retirees and people who work 26 miles away, in St. George, said Bruce Jones, one of the residents.
It's a community where the lots are big and hills and pinion and juniper trees create natural barriers between neighbors.
Jones lives an eighth of a mile from where Jorgensen and the others died. Jones said he was home Thursday, but didn't hear any gunfire or other sounds of trouble.
"We know a couple of people, but they're down the road a bit," Jones said.