A 20-year-old man suspected of firing shots that injured a woman and two children at Seattle’s Pritchard Island Beach on Memorial Day has been charged with assault.

Cedric Marvin Jackson III was charged with three counts of first-degree assault with a firearm enhancement, in King County Superior Court Tuesday afternoon, according to charging documents.

Prosecutors think Jackson, along with other people, “opened fire on unsuspecting families” swimming and barbecuing at the Rainier Beach park on Memorial Day. Seattle police are still investigating the shooting and have not said whether detectives are looking for other suspects or what they believe was the suspect’s motive.

Witnesses told police that two cars, which appeared to have multiple people in them, entered the park’s parking lot around 7 p.m. Prosecutors think Jackson was driving one of the cars, and one witness said he drove slowly through the parking lot, as if looking for someone, according to charges.

The cars stopped next to each other at the lot entrance, which is at the top of a hill looking down on the park. A witness said one driver, who police think was Jackson, got out of the car and began shooting down into the park. The witness told police there appeared to be multiple shooters but that the shots were coming from the car that police think Jackson was driving.

A 27-year-old woman was sitting in a car in the parking lot with her 17-month-old baby, preparing to leave the park. Both were struck by gunfire and suffered critical injuries. A 10-year-old girl was also shot; her injuries were not life-threatening.

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The people in the two cars drove away, and the victims were taken to Harborview Medical Center. The woman remained at the hospital in satisfactory condition Tuesday, hospital spokeswoman Susan Gregg said. The two children have been released.

About five minutes after the shooting, police received reports of an abandoned Cadillac that matched the description of the suspect’s car. They found it with a blown-out tire in the 7600 block of 48th Avenue South, about a mile from the park. The top of the car had fresh bullet damage, according to police.

Residents in that area told police that a driver and passenger got out of the car and ran down the street.

Detectives spoke to another witness who said she recognized one of the shooters when he drove by her. She told police Jackson was driving the car, and police found her description of Jackson and the car matched  those of other witnesses.

A detective found that Jackson’s mother lived a block from where the car was dropped off.

Detectives contacted the state Department of Corrections, because Jackson has been under supervision for a 2016 conviction for second-degree robbery, according to a department spokeswoman.

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The department happened to be sending officers for a regular check on Jackson’s Everett apartment. They followed Jackson as he got into someone’s car, which they later stopped to take Jackson into custody, three days after the shooting.

Police received search warrants and said they found a handgun stripped of pieces at Jackson’s mother’s house, a handgun at Jackson’s apartment and a loaded handgun in his backpack, which was in the car they arrested him in. Jackson is ineligible to possess firearms, according to court documents.

Jackson was booked into King County Jail, where he is being held in lieu of $500,000 bail.

He will appear in court again June 17.