The bodies of 44-year-old father Fernando Manrique, 43-year-old mother Maria Lutz, their 11-year-old daughter Elisa and 10-year-old son Martin were discovered in their Davidson home on Monday after police forced entry to the house.
The family's dog was also found dead inside the property in Sydney's north by officers responding to concerns for the family's welfare.
Authorities are refusing to say whether they are treating the deaths as a possible murder-suicide. There were reports there were no signs of violence or any visible injuries.
The children - in years four and five - both suffered intellectual disabilities and were students at St Lucy's in Wahroonga, a school for children with high complex needs.
The alarm for the Colombian family's welfare was raised after Ms Lutz did not turn up for her weekly shift in the school's canteen.
"One of the mums started to try and contact her and then we got worried so we called the police," St Lucy's acting principal Warren Hopley said.
The school has been devastated by the news.
"This is an exceptional family. They've been at the school here for six years. Two beautiful children. And mum was very active within the school - almost a cornerstone of the school in many ways," Mr Hopley said.
"I don't think she slept for many hours of the night because of the difficulties often with the two children, and yet she would always be here helping out in every way she possibly could."
Mr Hopley said he wasn't aware of any issues in the family.
"There was no inkling of any of this."
He spoke to the mother most days and says she was always positive, happy, friendly with other parents and greeted all 140 pupils by name.
The school's teachers were all upset and in shock, an emotional Mr Hopley said.
"The children had very complex needs so you become very attached to them," he said.
"This was an enormous, enormous shock. It was terrible."
The children were always active and friendly.
"The girl would often grab me by the hand and take me for a walk," Mr Hopley said.
"She had a very, really lovely personality and so did (her brother)."
Ms Lutz was last seen at the school on Friday having coffee with friends at the end of the day.
Police are refusing to reveal the manner, cause or possible motives for the family's death.
"We are gradually working our way through this very tragic circumstance,." Superintendent Dave Darcy said.
"I think it's just too early to be coming to conclusions.
"There is no one at the moment telling us what has happened. There's no one who has witnessed this."
Supt Darcy said the horrific discovery was extremely confronting for his officers.
St Lucy's is planning to hold a liturgy and prayer service to mourn the family's death at a later date.
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