Hyper-growth stocks can be fun and exciting. They can also be short-lived moths in Wall Street's winds. The best growth investors maintain a long investment horizon, looking for companies that combine stellar growth with long-term durability.

On that note, let me introduce you to a couple of my favorite high-octane growth stocks. Restaurant management software and language-learning apps may not sound like thrilling business ventures, but Toast (TOST 2.63%) and Duolingo (DUOL -1.53%) might just change your mind about that.

Toast's game-changing food service platform

It's not easy to manage a restaurant, a small chain of cafés, or a couple of drive-through fast-food spots. The business owner can end up with a point-of-sale system from Block, inventory tracking by Oracle's food and beverage segment, and a marketing campaign based on spreadsheets and hand-scribbled sticky notes.

Toast was born when its founders found it frustrating to make a quilt of separate restaurant software packages work together. The enormous food service industry was in dire need of a more user-friendly solution where every part of the system could refer to data from other components. So the same cloud-based platform that tracks ingredient inventories also handles order-taking and marketing-campaign designs.

Adding to the client-friendly nature of this software package, Toast also treats its order-taking and checkout hardware like a marketing tool. The hardware is sold below cost, giving businesses in the notoriously low-margin restaurant business another reason to check out what Toast can do for them.

Beyond that, happy clients tend to give Toast a good reputation locally. Word-of-mouth marketing is a powerful tool, and Toast explicitly aims to achieve it through heavy marketing pushes in specific geographical markets. Once the positive rumor mill is up and running, it's time to move the service-selling machine to the next city.

It's no surprise to see Toast's business skyrocketing. Trailing revenue has surged 87% higher in two years. The company is taking a pre-tax loss from operations, resulting in minimal tax expenses. At the same time, Toast's free cash flow is positive and rising.

The stock isn't even expensive. Trading at 3.7 times sales, Toast stock looks like a bargain in the context of soaring sales and rising cash flow. The time will come for positive bottom-line earnings, too, but Toast is still in the early innings of the classic growth-stock game.

I highly recommend buying some Toast shares while they're cheap. The $15 billion market cap you see today should balloon over time.

Duolingo's gamification approach to learning

Duolingo, the platform with the green owl mascot, has turned language learning into an addictive game. Every lesson feels like leveling up, with achievements, streaks, and that endearing owl cheering you on. It's not just about vocabulary and grammar; it's about conquering new challenges and earning virtual high-fives.

The company is revamping the very idea of learning by rote repetition. Gamifying this humdrum experience, with a healthy sprinkle of fun stories and friendly cartoon characters, makes the whole learning process fun, even addictive. With a daily learning streak that's likely passing eight years in June, I'm a walking illustration of Duolingo's habit-forming nature.

And I'm far from the only Duolingo devotee out there. The company sported 31.4 million daily active users in the first quarter, up from 20.3 million in the year-ago report. The number of paid subscribers also rose by 54%, landing at 7.4 million names. The lucrative portion of paid subscribers is rising, too, climbing from 8% to 8.6%.

I think it's just the start of a tremendous long-term growth story. Duolingo is already testing its gamified learning model in the fields of mathematics and music, presented in the same format as its language courses. Lessons learned from these experimental launches should help Duolingo expand into other repetitive learning opportunities over time, from world history to natural science and beyond.

The company isn't sitting on its green, feathered hands in terms of learning features, either. The Duolingo Max ultra-premium subscription plan lets you practice Spanish and French with an artificial intelligence (AI) chatbot. It can also explain your mistakes and expand on the lessons learned from a correct answer. I expect to see more AI-based learning tools from Duolingo over time, helping the company charge a premium price for extra-helpful services.

This stock isn't cheap. Duolingo trades at 13 times sales, 37 times free cash flow, and 185 times adjusted earnings. These are nosebleed valuation figures, reserved for the hottest of market darlings. But Duolingo deserves its premium share prices.

Users, revenue, and earnings are soaring, and Duolingo is staring down a massive global learning market. I can't wait to see where this wacky green owl will fly and how far Duolingo's $7.6 billion market cap can expand.