Nicole Jax jumped and flailed her arms with excitement each time she advanced a round on The Price is Right. But when the Waltham native won the grand prize, the Showcase Showdown worth $39,296, she froze and put her hands to her mouth in shock.

“I didn’t even know what to think,” she said. “I couldn’t fathom what was happening to me. It was a surreal experience.”

Jax, a 2012 graduate of Hayfield High School and now a freshman at South Dakota State University, appeared on the game show Tuesday morning and won a three-night stay in Los Angeles and a tour of the NCIS set, a six-night stay in Washington D.C. and a private tour of the city, and a 2013 Dodge Charger SE. During the first round of prizes, she also won a 55-inch 3D TV and nine seasons of NCIS valued at $2,182.

Jax was in L.A. with about 30 other students from her school’s dairy club, and they got tickets to a Jan. 8 taping of the show. She was one of the first four contestants chosen that day, and she won the second prize — the TV and NCIS box set — presented by Pauley Perrette, who plays Abby Sciuto on the show.

When she won the TV, Jax jumped up and down and pumped her fists to the point that the show’s host, Drew Carey, joined in.

“How are you doing?” he asked as she ran on stage.

“I’m really good,” Jax exclaimed.

Carey asked Jax where she is from and what she does, and Jax replied she’s from Waltham, Minn., and joked she does “a lot of things.”

“I do a lot of things. A little bit of this, a little bit of that,” Carey quipped back.

Jax then played for a chance to win $10,000. To win, she would have had to guessed which four of six grocery items had a retail price less than $7.50, but she guessed wrong on the third item, ending the game.

But as one of the first three contestants to advance past the first round, she got to spin the Price is Right wheel, where the winner advances to the Showcase Showdown to go head-to-head with one of the next three first-round winners.

Jax won, and the celebration continued.

“It didn’t even really register with me until [Carey] said I was going to the Showcase Showdown,” she said.

There, the other contestant bid $35,900 on the first prize package; a home gym, a free-standing fireplace and a 2013 Chevy Camaro Coupe LS. Jax got the second package, again presented by Perrette, and guessed its worth at $36,000.

Carey first revealed her package’s value and that she was low by $3,296, and finally that the other package is worth $27,440. Since that contestant guessed high, Jax automatically won.

“My friends [in the audience] were saying $36,000, but I thought that was low,” she said. “But it turned out I was right to trust them.”

Jax said she was immediately inundated Tuesday morning with phone calls, texts and Facebook and Twitter messages.

“By the first commercial, I had [26 messages],” she said. “My mom had 36 notifications on Facebook.”

By the end of the show, there were too many to count.

Many of her friends watched the show, and a class at Hayfield even took the period off to watch. Jax watched it in Waltham with her parents and grandparents, and said she’s glad she watched it with her grandfather especially, since they watched it together when she was growing up.

“I’ve been watching it so long at my grandpa’s, and we always competed against each other,” she said.

While Jax is forfeiting the trip to D.C. for tax purposes — and because she has been there twice in two years — she said she couldn’t be more excited for the trip to L.A., which starts Monday. She’s bringing her boyfriend, and they plan to hang out at the beach, go site seeing, and possibly catch a Hollywood movie premier.

And of course, she’ll get to see the NCIS set, although she’s not sure if they’ll meet the cast because the show’s filming schedule changes frequently. And while she doesn’t watch the show, she said it would be pretty cool to meet the actors.

The one thing she’s still undecided on: the Charger. Selling it would help pay for college, she said, but her parents say it might be fun.

“My parents kind of want me to keep it. I think they’re more excited about it than I am,” she said with a laugh.

What Nicole won

Nicole Jax, a 2012 Hayfield High School graduate, claimed the following prizes worth $41,478 on the Price is Right:

•2013 Dodge Charger SE

•3 nights at the Loews Hollywood Hotel in Los Angeles

•Limo ride to and from NCIS set

•Day on the set of NCIS and possibly lunch with the cast

•55-inch TV and nine seasons of NCIS