Just after noon last Sunday Bill and Anita Keeler finished counting the collection money at Schreiber Memorial United Methodist Church in north Dallas. Three blocks away, their son, David, waited for them at home.

The Keelers got into their car and drove north a mile to the Town North National Bank, just across the Lyndon B. Johnson Freeway, then turned back for the short drive to their ranch-style brick home on Ridgeside Drive. They arrived at about 12:15 p.m.

The Keelers walked into the hallway leading to the bedrooms. David, 14, was in his room. He was holding his father's Remington 1100 semi-automatic shotgun.

Police say they believe the first shots hit Bill Keeler, president of Arco Oil and Gas Co., in the chest and neck. David quickly reloaded investigators say. Anita Keeler was hit in the abdomen. David reloaded a second time and fired one more shot. He fled out the back door, leaving behind the weapon and seven spent shells.

At 12:40 p.m., Lee Walden, a patrolman with the Addison Police Department, was watching for speeders along a road about four miles north of the Keelers' home. A handsome teen-ager wearing blue shorts and a green sweatshirt rode up to the car on his green Schwinn Varsity 10-speed. Waldne rolled down the window and asked if he could help.

"I just shot and killed my parents at home with a shotgun," Walden reported David Keeler as telling him.

A week later, the mystery remains. More than a family has been shattered by the tragedy. A church, a school, a corporation, a neighborhood, a community, society asks the same question: what went wrong?

"you wonder, what is abnormal in the relationship of the family, what is out of sync?" said Methodist Bishop Ben Oliphint, a family friend. "You can't find it. Then you turn to the child and look, and you can't see it there either. That's the mystery."

Another close friend of the family said, "This was a beautiful child."

That is what is so baffling, and disturbing, to people who know the Keeler family. For a week they have searched their memories for clues to the reasons why the killings occurred, and have found nothing plausible, nothing out of the ordinary for an affluent, successful, loving family with a teen-aged son. Police who have talked to David have a similar reaction.

"He didn't tell me anything that was unusual for that kind of kid that age," said Jim Shivers of the Dallas Police Department. "Things just got on top of him."

In some cases like this there are simpler answers and clearer signposts: drugs, depression, failure, a history of antagonism between parents and child, scrapes with authorities.

In this case, the facts don't add up. David was bright, gentle, sensitive, athletic and talented. His first and only run-in with authorities, friends said, came on Saturday night, July 11, the night before the killings.

He and three others had been expelled from Six Flags Over Texas, an amusement park, for cutting into line at the Log Flume. When security guards picked up the boys, they found in the boys' possession several novelty items the boys admitted they had shoplifted, according to Bruce Neal, a spokesman for the park.

Park officials called Anita Keeler about 9 p.m., and at about 10:30 p.m. Bill Keeler picked up his son and two other boys and took them home.

The next day, David told an Addison policeman that his father was mad at him and that was the reason for the killing.

Bill Keeler was not the kind of man to get angry. "I never heard him raise his voice," Bishop Oliphint said.

Bill Keeler was born in Brownwood, Tex., 53 years ago, and earned an engineering degree from Texas A&M University. He joined Atlantic Richfield in 1949 as a junior engineer in Midland, Tex., and began a steady progression through the corporate ranks.

In 1973 he was named vice president of Atlantic Richfield Co. in Dallas, heading the firm's research, engineering and natural gas activities. The job gave him responsibility for the huge and complex engineering job of developing Arco's holdings in Prudhoe Bay in Alaska.

"It was an engineering and management enterprise of the first order," said Stuart C. Mut, a senior vice president of Arco Oil and Gas Co. "He was in the lead role during most of that period."

Two months ago, Keeler was named president of Arco Oil and Gas Co., Arco's largest subsidiary.

Keeler was well liked by his business associates. "He was a quiet, even-tempered, friendly sort," Mut said. "He was not flashy or demonstrative. I never remember him visibly upset or angry. He had the standard engineer's characteristics.

"He was logical and analytical in his approach. But he also had a good feel for other factors invovled in an enterprise, something not all engineers have. He had a good appreciation of the human factors involved."

Despite the enormous demands on his time, Keeler was devoted to his family, friends said. "I wouldn't say he found time for his family," Mut said. "It was an integral part of his daily life. He didn't take home a fat briefcase every night."

He was also active in his church, serving on various committees, welcoming new members, and, when he was promoted in May, his friends in the church rejoiced with him. "The feeling was that here was a good man who was also very able in his profession," said the Rev. Charles W. Cook, the church pastor.

Anita Keeler, 49, was even more involved in the church. She sang in the choir, served once as president of the United Methodist Women and was regularly around the church helping in any way she could.

She was an outgoing woman, effervescent, and she loved helping others. If an elderly peson needed a television set, she found one. If someone needed help shopping, she made sure it was done. Only a few days before the shootings, she bought flowers for a funeral of someone she did not know, after learning that no one else had sent any.

But the center of her life was her family. She and Bill had been married 31 years and had four children. Barbara, 27, who works for the Environmental Protection Agency's regional office in Dallas; John, 25, who is finishing up his education and lives in the Dallas area; Robert, 19, a sophomore at the University of Texas in Austin studying geology and described as "the epitome of the All-American Boy," and David.

Life at the Keeler home revolved around the children, with vacation camping trips to Lake Ouachita in Arkansas, dove hunting in west Texas, golf at the country club and attendance at the children's games.

Anita rarely missed a football, basketball or baseball game that involved one of her children. Bill sometimes went straight from an airplane to the playing field.

On most Sundays, even after Barbara and John had moved away, the family would gather for the afternoon at the house on Ridgeside Drive, where they swam in their back-yard pool. When Robert went off to college last fall, Anita wrote to him every few days, and Bill called his son once or twice a week, friends said.

They lived comfortably, but not ostentatiously. The homes in their neighborhood are valued at $150,000 to $180,000. And even though they were well off, Bill looked for ways to make the pinch of private school tuition less severe. When he drew up his will, he was particularly concerned that the two younger boys would be assured of a quality education.

David, the youngest of the children, attended St. Mark's School of Texas, one of the best private schools in the city. He was an honor-roll student and a good athlete who played on the football and basketball teams.

Earlier this summer, he had helped out as a counselor at the school's summer camp. "He was one of the best and the brightest," said George Edwards, head of the high school at St. Mark's that David would have entered this fall.

David also was active in church affairs, working at vacation Bible school this summer, involved in the church youth group and a regular in the teen-age pews on Sunday morning. "I don't suppose any teenager is around the church more than he is," Pastor Cook said.

David has told police that there have been problems with his parents for almost two years, but to outsiders they sound like the woes of normal adolescence. He reportedly told one friend, "My parents won't let me go where I want to go or do what I want to do."

His mother, who nagged him occasionally, was concerned that David seemed to withdraw into his room more in the last year. David had problems in a math class at St. Mark's this year, a family friend said, but added that many other children in the class had had problems.

Whatever rage was building up inside David was never noticed by those around him.

What happened after the Six Flags incident also is not clear. It is not known what punishment David's parents had planned for him, and it is doubtful that they had told David. It is not even clear that there had been a real argument over the incident.

There had been little time to talk out the matter from the time Bill Keeler picked up his son that Saturday night and the end of church services the next morning, and friends had stayed overnight with David. Bill Keeler's anger may have been more felt by David than expressed.

Barbara Keeler discovered the shootings about 15 minutes after they occurred. When she got no answer at the front door of her parents' house, she entered and found them on the floor in the hallway. Her father was dead, her mother dying. Anita Keeler said to her daughter: "David. David. David did it."

David Keeler is now in custody in the Dallas County Juvenile Detention Center facing charges of delinquent conduct, in accordance with the Texas penal code.