As the old saying goes, math is like love—a simple idea but it can get complicated. This is true more so than ever when it comes to the quadratic equation, a concept commonly introduced in beginning algebra classes. Unfortunately, obtaining a strong understanding on the quadratic equation is essential for students who wish to pursue higher education in the field of science, math, engineering, or information technology. Individuals who wish to learn more about the quadratic equation can typically do so by talking to math instructors at local high schools, technical colleges, or universities. In addition, online resources or used textbooks may also be able to provide some guidance when it comes to mastering this challenging topic.

**Overview of the Quadratic Equation**

According to most mathematicians, the quadratic equation is defined as “a univariate polynomial equation of the second degree.” In other words, this means that it is an equation in which there are several terms, one of which is squared, and the user is typically asked to solve for the variant, “x.” Though initially introduced during beginning algebra classes, the quadratic equation is also used extensively in calculus, trigonometry, and other advanced mathematics platforms. Students who do not master the basics of the quadratic equation in its simpler form are likely to experience challenges when the formula is highly developed. These individuals should seek assistance from a teacher, friend, or family member as soon as possible to avoid further confusion regarding the topic.

**Quadratic Formula**

Traditionally, the quadratic equation is written as “ax2 + bx + c = 0.” While there are a number of methods of solving the quadratic equation, the most popular involves the use of the quadratic formula. Traditionally, the quadratic formula is written as either “x = -b + (the square root of b2 – 4ac) / 2a,” or “x = -b – (the square root of b2 – 4ac) / 2a.” It is important for students who are new to the quadratic equation to understand that in most cases, only one of these formulas will produce the correct answer. Individuals interested in the quadratic formula should become familiar with both of these techniques to ensure optimal results.

**Quadratic Factorization**

Quadratic factorization refers to the process by which the quadratic equation can be solved without the use of the quadratic formula. Most experts agree that there are two different methods that can be used during quadratic factorization, including “completing the square,” and factoring by guessing. In both of these methods, common factors are removed, making it easier to determine the variant, “x.” While “completing the square” and factoring by guessing are often easier than the quadratic equation, they are not always as accurate. In most cases, they are only effective for beginning, basic quadratic equations.

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- Solving Quadratic Equations by Factoring: A Handout from Learning Assistance at Trident Technical College
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**Applications of the Quadratic Equation**

While the quadratic equation is traditionally taught in the setting of an algebra or calculus classroom, it does have a number of applications outside of the school building. Specifically, the quadratic equation appears to be quite useful in the concept of acceleration, velocity, and stopping power, making it essential for individuals who are interested in auto mechanics, engineering, and vehicle repair. In addition, the quadratic equation has been found to be widely evident in a number of natural processes. Some of these include the processes by which light is reflected off a lens, water flows down a rocky stream, or even the manner in which fur, spots, or stripes develop on wild animals. As research regarding the quadratic continues, it is likely that more and more applications of this equation will be recognized, making its comprehension even more essential for individuals who strive to make a difference in the world of science, math, and engineering.

*Written by Grace Ann Stanford*