City officials brushed off parents’ concerns over an ongoing cheating investigation at a Bronx high school last night, telling them that if the principal had really been changing grades, the school wouldn’t be failing.

In 2009, teachers at Herbert Lehman High School reported that executive principal Janet Saraceno was changing dozens of students’ grades in order to boost the school’s graduation rate. More than a year later, Saraceno remains under investigation and Lehman is teetering on the edge of being shut down by the city after receiving an F on its progress report. Yet when parents asked Department of Education officials about the investigation at a meeting last night, they were told to ignore it.

“Let’s let the investigators do their work,” said Juan Ruiz, a DOE official heading the team assigned to support Lehman. He told parents that if Saraceno had really been changing students’ grades from failing to passing, “we probably wouldn’t have an F.”

In fact, Saraceno is only under investigation for changing grades during the 2008-09 school year and Lehman’s progress report grade for that year was a B. A year later, after DOE officials became aware of the cheating and began to monitor the school more closely, its grade fell to an F.

Last night’s meeting was a chance for city officials to explain to parents what might happen to Lehman in the next year. Yet after an hour, parents began walk out, frustrated their questions weren’t being taken seriously.

“Where are the weaknesses? I want to know how it went from a B to an F,” said a parent.

Reading from the DOE’s fact-sheet, Bronx high school superintendent Elena Papaliberios said that Lehman students weren’t passing enough of their classes — one of the metrics the city uses to gauge how well a school is doing.

“Even as they finish their first year, they’re starting to struggle,” she said. “And if they don’t earn 10 credits per year, they’re going to fall short and they’re not going to be able to graduate.”

Parents of Lehman students have been stunned by the school’s precipitous decline, as it has long been considered one of the city’s best remaining large high schools. For 29 years, Lehman was run by former principal Robert Leder, who resigned in 2008. Since then, safety has become a problem and this year the school installed metal detectors. Teachers and students say the new principal rarely leaves her office and does not have the rapport with students that Leder used to keep the large population — 4,000 students — under control.

Ruiz said the city planned to reduce the school’s enrollment next year and that the metal detectors have already cut down the number of violent incidents.

Elvin Flores, the father of a Lehman freshman, said his daughter graduated from the school five years ago without incident. But from his son’s first day of school this year, there have been problems with safety.

“How the heck did you guys lose control of this school?” Flores asked. “For the years Leder was here, we felt safe. You guys need to take back this school.”

Parents at the meeting said when they visited the school during orientation, classroom walls were hung with students’ work that was two years old. Others said they’d gone to parent association meetings hoping to meet the principal, only to watch her rush out afterwards.

Saraceno sat at the front of the auditorium and did not speak, except to say that the school’s graduation rate was 52 percent rather than 49 percent, the number Ruiz gave.

“She’s sitting there and not saying anything,” said Lisa Mateo, whose daughter is a freshman at Lehman. “By now she should know she looks guilty.”