Quadratic equations is an important math topic that finds its applications in many different fields. It is widely applied in many ways, from calculating the profit on products to determining values like speed, area, or other dimensions of the various objects. Hence gaining an in-depth understanding of quadratic equations and their applications is crucial for every student.

What is a Quadratic Equation?

A quadratic equation is an equation that has at least one squared variable. The quadratic equation is represented in its standard form as px² + qx + r = 0, where x is a variable with unknown value, and p q and r are the coefficients representing known numbers letter ‘p’ is not equal to zero.

Applications of Quadratic Equations:

Some of the most common applications of quadratic equations in the field of engineering, sports, and management to estimate various quantities like speed, area, profits, and so on. Here are a few ways we use quadratic equations in real-life:

In Finding Areas

We frequently use quadratic equations to calculate the area of various objects like rooms, plots, boxes, etc. One example that depicts the practical use of quadratic equations is making a rectangular box with one side twice the length of the other side. If we have only four square feet of wood for the base of a wooden box, we can apply this information to create an equation that determines the box’s area. As per the ratio of the two sides, the area will be the length times the width– in terms of x would equal x times 2x, or 2x^2. This equation will be less than or equal to four to build a box by applying these constraints.

Determining Profits

Quadratic functions are also used in calculating a business profit. For example, if you are selling something as simple as cookies– you need to decide how many packs to produce so that you can get a profit. Let’s assume you’re selling packs of cookies, and you want to make 12 packs. However, you can sell different numbers of packs depending on the selling price you pick. For $100 per pack, you’re not likely to sell any, but at $0.4 per pack, you’ll probably sell 12 packs in less time. So, to decide the price, use X as a variable. You’ve estimated the demand for a pack of cookies to be at 12 – X. Your income, therefore, will be the price times the number of packs sold: X times 12 minus X, or 12X – X^2.

Finding Speed

Quadratic equations are also useful in calculating the speeds of moving objects like cars, airplanes, trains, etc. For example, quadratic equations are used to estimate the speed of a boat going up and down a river. Another example of the use of quadratic equations is to determine the speeds of cars involved in accidents on the road by traffic police.

Career In Engineering

Quadratic equations are used in engineering more than any other branch. These equations are vital to design curved equipment and other structures. Brake systems in cars are designed by automobile engineers by solving quadratic equations. Aerospace engineers also use quadratic equations in their careers. Chemical and electrical engineers apply quadratic equations to solve the complex system—audio engineers design sound systems with the help of solving some equations.

Management Work

Plenty of management work involves the use of quadratic equations every day. For example, managers, supervisors, and engineers deal with these equations on a daily basis to manage people and resources. This means they require a good understanding of quadratic equations. For instance, HR managers evaluate the workforce needed to accomplish a certain task. Additionally, they must have the skills to calculate salaries or to build pension plans. All such activities are mostly based on the applications of quadratic equations. Insurance agents also deal with them because they have to design complex insurance models and plans that involve a lot of computation.


Learning quadratic equations is important for a career as well as for understanding its real-life applications. Cuemath helps students to understand math logically by strengthening their reasoning skills. With Cuemath methodological learning, students can gain a sound conceptual knowledge of this topic that enables them to connect between various math topics and their applications.