In this image provided by Facebook, Facebook founder, Chairman and CEO Mark Zuckerberg, center, rings the opening bell of the Nasdaq stock market, Friday, May 18, 2012. (Zef Nikolla/AP)

After a market debut marred by technical glitches and a deep dive in the company’s stock price, Facebook has spent the past year focused on its biggest weaknesses: how to make money and keep its more than 1 billion users tethered to the social network.

The results have been mixed. The company’s stock price has recovered some of its worst losses, and Facebook has announced several moneymaking initiatives. But the circumstances surrounding the IPO are still under investigation by the Securities and Exchange Commission, and some investors remain unconvinced the social network has staying power.

Facebook’s market debut last May was supposed to be the coming-of-age moment for a new generation of tech companies and a surefire bet for the small investor.

Instead, doubts about whether the young company was mature enough to meet shareholders’ demands helped send the company’s shares down from its opening price of $38 per share to a low of $17.55 in August. Although the stock has recovered over the past six months, it’s still about 30 percent below its initial price.

To answer its skeptics, chief executive Mark Zuckerberg has focused on developing Facebook’s mobile platform first and ordered mobile-friendly redesigns of just about everything. Facebook’s news feed, the running list of updates from friends, now has bigger pictures, which pop on small screens. And on its smartphone apps, it has increased the size of its photos and made it easier to navigate through friends’ updates with the swipe of a thumb.

How tech stocks fared in their first years.

It has also tackled a perhaps bigger problem: convincing investors that it can pump up its advertising revenue. Facebook dipped its toe into commerce, allowing retailers to sell gifts to its users through the site. It also introduced new types of ads that allowed advertisers to more directly target users.

The company made 30 percent of its $1.25 billion in ad revenue in the past quarter through mobile ads. Nine months ago, those mobile products didn’t even exist.

The company has “spent the last year catching up to ads in the rest of the industry,” said Forrester Research analyst Nate Elliott. “They’ve done a great job of making their offerings comparable.”

But there is still more to do, Elliott said. The company should make more of its rich social data available outside the confines of its own site, he said.

The flubbed IPO has left a bad taste in the mouths of retail investors, who felt burned by the way the company and bankers handled the deal, said Andrew Stoltmann, a Chicago-based securities lawyer.

“The damage done by the Facebook IPO was pretty wide and still reverberates in the market now,” he said. “Most investors who invested in Facebook have not made their money back.”

The botched debut also drew scrutiny from the SEC. The agency is investigating whether Facebook and the underwriters it worked with selectively disclosed information immediately before the IPO about Facebook’s money-making prospects.

The SEC is also probing whether Nasdaq bears responsibility for the technical problems that plagued the exchange when Facebook started trading, costing many firms millions of dollars.

In March, the SEC approved a plan proposed by Nasdaq to pay qualified customers $62 million to make up for the losses. But some firms may seek more.  Switzerland’s UBS AG has said it is taking legal action to get fully reimbursed for its losses, which it had once said totaled more than $350 million.

(Washington Post Co. chairman and chief executive Donald E. Graham is a member of Facebook’s board of directors.)

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