Despite fears about a potential recession and increasing political uncertainty in the United States, the stock market continues to chug along. The benchmark S&P 500 index is up about 13% over the past 12 months.

These gains likely have some investors looking for companies that are best-positioned to benefit from the market's upward trend. If you're in search of growth stocks underpinned by strong businesses with big opportunities, look no further than HubSpot (NYSE:HUBS), Shopify (NYSE:SHOP), and Square (NYSE:SQ).

Image of a rocket taking off from its launchpad.

Image source: Getty Images.

HubSpot

If you've been watching HubSpot's recent stock performance, you may be surprised to see it on this list. After all, its share price has fallen by 25% over the past three months.

But if you look a little closer at how this cloud-based marketing platform company is doing as a business, you'll see that the recent selloff of HubSpot's stock was likely overblown. In its third quarter, sales increased by 32% year over year, and the total number of customers rose by 31%.

Additionally, its main revenue source, subscription services, grew by 33%, and management expects total revenue to increase by 25% -- at the top end of its previous guidance range -- in the fourth quarter.

So if the company is still growing at a healthy clip, why the recent share price drop? That likely can be traced back to the hit that the broader software stocks sector took recently. Based on HubSpot's recent growth rates, and the fact that its shares are trading at a significant discount to where they were a few months ago, now may be a good time to snatch up this stock. 

Shopify

Revenues for Shopify, the e-commerce platform company that helps businesses of all sizes set up and manage online stores, have been rising at a meteoric pace, and that continued in the third quarter. 

Its sales skyrocketed by 45% to $390.6 million, exceeding both the consensus estimate of Wall Street analysts and the company's own guidance. The company's two core revenue segments, subscription solutions and merchant solutions, grew by 37% and 50%, respectively. Additionally, Shopify reached an impressive milestone: It now serves more than 1 million merchants worldwide.

That strong Q3 performance led management to raise its full-year revenue outlook from the previous range of $1.51 billion to $1.53 billion to a new range of $1.54 billion to $1.55 billion.

Shopify's shares have been volatile over the past three months, but that shouldn't scare investors away. The company's fortunes are tied to the growth of e-commerce, which is still in a relatively early stage in the U.S. Only 11% of all retail sales in the U.S. occur online right now, which leaves plenty of room for the e-commerce market, and Shopify, to continue growing.

Square

Square, which sells hardware and software that allows businesses to accept electronic payments, is benefiting from the rising popularity of digital payments and e-commerce. And the company's third-quarter results exemplified its impressive growth story. 

During the quarter, Square's adjusted revenue rose 40% to $602 million, topping analysts' consensus estimate of $596 million. Total sales growth was powered by subscription and services revenue, which jumped 68% from the year-ago quarter. 

Additionally, the company's non-GAAP earnings per share also beat analysts' estimates, growing 92% year over year to $0.25. Square's gross payment volume -- the amount of money spent on its payment platform -- increased 25% year over year. And if all of that weren't enough to get investors excited, Square's net income was $29 million in the third quarter, up from $20 million in the year-ago quarter.

The payments company is experiencing a surge of growth right now, and there's likely more to come. The company is firmly embedded in the peer-to-peer payment market and the broader digital payments market, which will be worth an estimated $7.6 trillion worldwide by 2024.

Growth stocks also mean volatility

The fact that all of these companies are operating in growth mode right now means that they're likely to experience some share-price volatility along the way. Just as has already happened with HubSpot,  investors may react to broader market trends and push their share prices down for seemingly no reason. Investors should keep in mind why they're buying these growth stocks, remember to hold onto them for the long haul, even if the ride gets a little bumpy.