Alex Smith, 34, has impressed his teammates with a work ethic and quiet confidence developed over 13 years as a pro. (Toni L. Sandys/The Washington Post)

For the past six years, the Redskins went through a gamut of tumult and drama — much of it self-inflicted — while attempting to develop two quarterbacks from one draft class. First there was Robert Griffin III, an instant success who was incinerated by the flames of his own rising star and ultimately undone by injuries that were exacerbated by Washington’s institutional dysfunction. Then there was Kirk Cousins, the unlikely successor whose willingness to bet on himself grew into a lucrative exit strategy.

By acquiring Alex Smith from Kansas City this offseason, the Redskins have introduced a leader into their locker room who, compared to his predecessors, must seem like a steady, stoic stepdad ready to put an end to the family’s feuding ways.

Cast out by Kansas City after completing the finest season of his 13-year career, Smith offers Washington something the city hasn’t truly had since the Redskins last hoisted the Lombardi Trophy on Jan. 26, 1992: A fully formed franchise quarterback who’s committed for the long haul.

While Cousins’ critics say he wasn’t being authentic when he insisted he wanted to stay in Washington, Smith told reporters at his introductory news conference in March, “This is where I wanted to be.”

In their own ways, Griffin and Cousins were big talkers. Griffin, who’s now a backup quarterback in Baltimore, talked up his catchphrases and brand — and he had a habit of blaming his teammates’ shortcomings. Cousins, who’s now tasked with guiding a Super Bowl contender in Minnesota, talked about seeing the world in 15-minute increments, hunkering down in a film-watching nook and how, gee, he’d really love to stick around if the Redskins would just break the bank instead of asking him to play under the franchise tag for two straight seasons.

Since Smith’s arrival in a deal that sent promising cornerback Kendall Fuller and a third-round pick to the Chiefs, Washington’s new quarterback has won the respect of the locker room with what he’s left unsaid.

“He just came in, and he was quiet,” running back Chris Thompson said. “He just let everything work itself out. He got a feel for everybody, and then that’s when he started talking more to guys. I think everybody respected that about him. He didn’t come in and was like, ‘This is my team, y’all need to get behind me,’ and blah blah blah. It wasn’t like that. It was like he was coming to a new team, getting to know everybody, and people just respected that about him.”

Money talks, too, of course, and the Redskins’ willingness to pay Smith left critics questioning the club’s decision to splurge on a quarterback who is four years older than Cousins but whose strengths and weaknesses are fairly identical. Smith, 34, received a four-year, $94 million extension from the Redskins. Cousins, 30, got a fully guaranteed three-year deal worth $84 million from the Vikings.

What Smith’s new teammates observed from the earliest offseason workouts was a veteran whose meticulous training habits helped him navigate 13 years in the NFL.

The fact that Smith, who was selected No. 1 overall by the 49ers in the 2005 draft, is still in the league is remarkable considering that he didn’t quarterback San Francisco to a winning record in any of his first six years, which included a full season lost to a shoulder injury. Once Jim Harbaugh became coach in San Francisco, Smith led the 49ers to a 13-3 record and their first playoff win in nine years.

A concussion Smith suffered the following season opened the door for Colin Kaepernick to elbow Smith out of the job, and Smith was traded to the Chiefs in 2013 for two second-round picks.

In five seasons with Kansas City, Smith was one of 12 NFL quarterbacks to start at least 76 games. He threw the fewest interceptions (33) of anyone on that list. He also threw the second-fewest touchdown passes (102) — only Joe Flacco tossed fewer. As the Chiefs’ starter, Smith won 50 regular-season games, made three Pro Bowls and led Kansas City to the postseason four times. Last season, he led the NFL in passer rating with a mark of 104.7.

But his 1-4 playoff record with the Chiefs left the team unsatisfied, and for the second time in his career, he was traded away.

No one would be able to survive so many years in the pressure cooker that is life in the league without developing a thick skin.

“I don’t feel like I have to prove myself to anybody any longer,” Smith told The Washington Post this summer.

So when it came time for Smith to make a first impression on the Redskins’ locker room, he didn’t need to campaign for himself. All he needed to do was go about his business as usual.

Safety D.J. Swearinger noticed how Smith’s command of the huddle settled the offense, how Smith was looking off safeties and making smart decisions with the ball in practice.

“A lot of it isn’t even him trying, it’s just him being himself,” Swearinger said. “We respected him as soon as he stepped in.”

Linebacker Mason Foster noticed how Smith pushed himself in everything he did.

“From Day 1,” Foster said, “he came in in OTAs running and competing in every drill, in there lifting all the time, working hard, just a straight winner. It’s the same thing you see on film.”

The longer Smith spent around the guys, and the more his on-field communication revealed his intellect, the more Smith began to let his leadership style show. And although Smith had limited snaps in an underwhelming preseason, his presence gives teammates confidence that the Redskins will be competitive this season.

“When practice is going bad — even when it’s going good — he’ll say something, you know just a quick two or three words. It’s not much, but you just kind of feel it,” Thompson said. “That’s something that comes from a guy that’s been in the league for a very long time. You know there’s a reason that they’re still in the league.”