An officer arrives and addresses Coignard, who appears to show him her palm. The officer struggles with the teen, forcing her into a chair, then down to the ground. She reaches for the knife, and the officer draws his gun.

As two more officers arrive, Coignard stands and charges at the first officer, who opens fire. Coignard falls to the floor, struck four times.

As colleagues comfort the officer, paramedics arrive, perform CPR on Coignard and carry her body away on a stretcher.

Longview Police Chief Don Dingler has defended the officers’ actions. The video shows “time was a factor,” Dingler told reporters. “There was no time for the officers to use other means.”

Coignard’s parents strongly disagree. Though they are baffled by their daughter’s actions that day — was it a suicide attempt? — they don’t understand why three officers couldn’t subdue their slight, teenage daughter without resorting to deadly force.

Whatever her motives, “she should still be here,” Erik Coignard said. “She was asking for help, and she was failed when that officer failed to take control of the situation. . . . This shouldn’t have ended this way.”

Mental health experts say most police departments need to quadruple the amount of training that recruits receive for dealing with the mentally ill, requiring as much time in the crisis-intervention classroom as police currently spend on the shooting range. But training is no panacea, experts caution.

The mentally ill are unpredictable. Moreover, police often have no way of knowing when they are dealing with a mentally ill person. Officers are routinely dispatched with information that is incomplete or wrong. And in a handful of cases this year, police were prodded to shoot someone who wanted to die.

That was the case with Matthew Hoffman, a 32-year-old white man who had long struggled with mental illness, according to family members. After breaking up with his girlfriend, Hoffman walked up to San Francisco police officers in January outside a police station in the bustling Mission District. He pulled a gun from his waistband, pointed it at the officers and advanced in silence.

The startled officers fired 10 shots, three of which struck Hoffman. They later discovered that his weapon was a BB gun. And they found a note on his mobile phone, addressed to the officers who shot him.

“You did nothing wrong,” it said. “You ended the life of a man who was too much of a coward to do it himself.”

Grace Gatpandan, San Francisco Police Department spokeswoman, said the department offers crisis-intervention training. But those classes are designed primarily to teach officers to handle someone threatening to jump off a bridge, not someone pointing a gun in a crowded tourist area.

“When officers are faced with a deadly situation, when there is a gun pointed at a cop, there is no time to go into mental health measures,” Gatpandan said. “There was nothing we could have done. This is one of those tragedies.”