NEW YORK — Who were those willowy young women with Barack and Michelle Obama — and where’d they hide little Sasha and Malia?

Four years is a long time when it’s a half or a third of your life, and so TV viewers who hadn’t seen the Obama girls much since 2008 might have been truly startled at just how much they’d grown when they appeared onstage with their father last week.

After all, Malia, now 14, who started high school last week, was just about as tall as her already tall parents.

Relaxed and composed, in a sleeveless dress from H&M, Malia laughed with her father onstage after his remarks, and earlier sat and applauded with her mom and her sister, Sasha, who wore a print frock from Anthropologie.

What struck one former White House aide was the ease and comfort with which the girls were inhabiting their public roles.

“Their smiles were genuine and huge tonight,” said Anita McBride, a former chief of staff to Laura Bush, as well as an assistant to Bush’s husband. “There was no awkwardness. They clearly have adjusted to their life in the public eye.” McBride said she was also stunned by how poised and grownup the girls looked.

One reason the scene was so striking is that the American public doesn’t see the daughters regularly, especially on TV. “There hasn’t been a steady stream of images to relate to,” said Sandra Sobieraj, a correspondent for People who covers the first family.

For the president and first lady, protecting their privacy has been an evolving skill. Candidate Obama quickly regretted, for example, an all-family interview granted to the TV show “Access Hollywood.”

Once the family arrived at the White House, strict arrangements were in place. The news media traditionally respects the privacy of a president’s young children and doesn’t photograph or report on them unless they are in a public setting with their parents.

Yet the couple constantly talks about their kids. At times the president has embarrassed them, as when he told an audience that Malia once got a 73 on a science test. (He later apologized.)

Two years ago, when Malia first went to summer camp, the White House discouraged mention of it in the media, even though Obama mentioned it in interviews. And recently he revealed the state where both daughters had just spent a month at camp — New Hampshire.

Whereas many White House children through history seem to suffer some sort of embarrassment or scandal, the Obama girls have had none.

“Compared to other White House families, this is clearly the most functional,” said Doug Wead, who chronicled a host of misfortunes of past White House kids in his book “All the President’s Children.” (He’s now working on a book about White House siblings.) “This has been one of the most successful stories.”

McBride, who now directs programming on the history of first ladies at American University, says that no matter your politics, it’s comforting to see a happy first family. “Whether you support this president or not, you want to know that it’s healthy and grounded and going well at home. They clearly are a family that’s got it together.”