Austin, a liberal college town and the seat of state government, is perhaps best known for its hip counterculture, live music and string of successful high-tech companies.

Fast cars? Not so much.

But in a couple of weeks, the state capital will become the epicenter of the auto racing world when its gleaming new $400 million track — the Circuit of the Americas — hosts the first Formula One race in the United States since 2007.

For top drivers like Sebastian Vettel of Germany and Fernando Alonso of Spain, the Nov. 18 race offers the second-to-last chance to improve their standing in the coveted F1 championship — arguably the most prestigious prize in motorsports — on a track boasting one of the most challenging turns in the world.

But for the host city, it will be an opportunity to prove that screaming-fast race cars and the well-heeled clientele that follows them around the globe will be welcome in a town that made a homeless transvestite a local celebrity, and whose most famous bumper sticker is “Keep Austin Weird.”

“It’s a new stage of life for the city of Austin,’’ Mayor Lee Leffingwell said. “We want to keep what’s good about Austin, but we also want to be open to new things.”

City planners and race promoters have their work cut out for them. They will still have to work out any last-minute kinks on a project that was beset with construction delays and uncertainty about tax incentives. Fears of a monster traffic jam and complaints from skeptical neighborhood associations and community activists also have race backers on edge.

Some 120,000 people are expected to pack the state-of-the-art facility for the two-hour race, and thousands more will attend a series of sideshows, musical performances and fan fests during the three-day event. Underscoring the deep music culture of the city, Willie Nelson will headline a concert in downtown Austin on Nov. 15 to help kick things off.

The design of the twisting 3.4-mile track takes inspiration from some of the world’s most famous F1 venues, including England’s Silverstone, Brazil’s Interlagos and Istanbul Park in Turkey. The signature feature of the Circuit of the Americas track, Turn 1, has been compared to Austria’s famed Red Bull Ring — only more difficult. The cars, over dozens of laps, can reach speeds in excess of 200 miles per hour.

“To have that steep of a hill right beyond the start-finish line is pretty much unique in Formula One,” said Bob Varsha, longtime F1 announcer for the Speed network, which will broadcast the Austin race. “At the top this hill is a very sharp braking area for a left hand hairpin, and then plunging downhill.”

The state estimates the event will pump more than $200 million into the Texas economy as visitors pay increased hotel rates, buy local products and stage exclusive parties.

Unlike the U.S.-based NASCAR series, which tends to attract a beer-drinking, blue-collar crowd, Formula One has cultivated a more glamorous, international image. As part of the deal to land the Formula One race in Austin over the next 10 years, Circuit of the Americas had to build 12 spacious suites — known as the Paddock Club — where patrons will plunk down more than $4,000 each to watch the race while consuming champagne and hors d’oeuvres.

Helicopter charter companies are hoping to do brisk business ferrying the jet-setters to and from the track, which has six helipads.

“They don’t want to sit in traffic, and they can afford to pay the ticket price in and out,” said Randy Riggs, owner of Austin Helicopter Tours. The round trip fare, for about 10 minutes in the air, is $545.

Homeowners eager to cash in have not been as successful. Advertisements for house rentals for as high as $6,000 a night — some with airplane hangars and helicopter landing pads — have gone unanswered, but fans are snapping up RV sites on austinracerentals.com, which caters to F1 visitors.

“Right now the ones that are cheaper are going the fastest,” said Danielle Crespo, who owns the website. “I think there was a misconception that there wouldn’t be any hotel rooms available and everybody was having champagne and caviar for breakfast. That’s just not the case.”

The race will mark the end of a long journey to re-introduce Formula One in the United States. While popular globally, the upscale racing series has been eclipsed in the United States by NASCAR. The last F1 race in the country was in 2007 at the Indianapolis Motor Speedway.

Eager to get back into the lucrative U.S. market, Bernie Ecclestone, the chief of Formula One, signed off on a deal in 2010 to bring F1 to Austin on the first American track built specifically for open-wheel Formula One race cars.

But a series of setbacks almost derailed it. Contract negotiations dragged on longer than expected, bitter legal wrangling caused construction delays and State Comptroller Susan Combs withdrew a pledge made in May 2010 to grant a taxpayer subsidy worth $250 million over 10 years.

As it turned out, no local entity had signed off on the deal as required under Texas law. And once the Austin City Council examined the particulars, members balked at coughing up the city’s $4 million contribution, an amount equal to the expected sales tax revenue the out-of-town F1 visitors are expected to generate.

Tea Party activists and lawmakers did not like the subsidy deal, either, and they are vowing to fight such tax incentives — along with a slew of others — when the Legislature reconvenes in January.

In the meantime, at least for the first race, the F1 track owners have taken care of the $4 million contribution the city was supposed to chip in and now expect to get the estimated $25 million state tax incentive payment the old-fashioned way — after the first event is held and the economic impact is measured. It is the same process the state has used when the NCAA college basketball tournament and the Super Bowl were held in Texas.

“We wouldn’t have gone forward without the state as a partner, because economically it doesn’t make sense for us,” said Bobby Epstein, who, along with the Texas billionaire Red McCombs, is one of the largest investors in the track.

Epstein, 47, had planned on building a housing development on the property in southeastern Travis County when he was approached about the project. He did not know much about race cars, but he quickly saw the potential to create a world-class entertainment complex in fast-growing Central Texas.

Now Epstein sees the 1,200-acre facility, which has more than 200,000 square feet of indoor meeting space and 25,000 parking spots, as an economic engine for the region. Circuit of the Americas has already booked four non-F1 racing events, including the MotoGP motorcycle race in April.

An amphitheater, modeled in part after the Hollywood Bowl, can accommodate 15,000, and Epstein has already inked a deal with Live Nation to bring top-name musical acts to the venue.

“I hope the music fan looks at it and says, ‘This is the best music venue I’ve ever been to. And oh, there’s a race track around it,’ ” Epstein said.