# Getting started with usage of the quadratic formula calculator

• In order to take advantage from the quadratic formula calculator, you need to make sure you have all the necessary data to use in that or another formula. All the data has to be provided within the given assignment.
• Once you figured out the needed data, you have to enter the quadratic equation of the specific form into the quadratic formula calculator.
• After that, you need to pick up the task that you want the quadratic formula calculator to deal with.
• There are four kinds of problems that we have already mentioned above, so you need to choose which one is what you need to solve.
• Once the problem is chosen, the quadratic formula calculator will proceed to the solving.

As you can see, the process of using the quadratic formula calculator is rather simple and its usage doesn’t require any specific skills or knowledges. Quite the opposite, absolutely everybody can succeed with the quadratic formula calculator, because it takes only a minute to achieve the needed result without spending significant efforts or applying specific skills.

In terms of elementary algebra, the quadratic formula represents the solution of a particular quadratic equation. On the one hand, this formula is not the only way to solve the mathematical quadratic equation, as long as there are also other ways that may be used and lead to the achievement of the same result. These ways are such as graphing, factoring, completing the square, etc. On the other hand, however, the usage of quadratic formula is the most popular way of solving quadratic equations for the reason that this is the most convenient, quick and effective way.

For driving the quadratic formula the first and the most important thing that a student has to understand is the process of completing a square. This circumstance serves as a reason for the fact that many students don’t learn derivation as a part of practicing and exercising and they often proceed right to the formula without understanding other steps that the process of solving of a quadratic equation may include.

As for the quadratic equation, in terms if elementary algebra it can be any kind of equation, as far as it has the following form: ax2+bx+c=0. In this form, x serves to represent something that we are looking for, while a and b serve to represent the given numbers that we already know and that are not equal to zero. Due to the fact that the quadratic equation always has only one unknown element, it is often called as «univariate». One of the methods that the quadratic equation can be solved with is a specific process that is widely known as factoring. The best way to solve it, as we have already said, is the quadratic formula.

## Historical development of the quadratic formula

Since the beginning of usage of mathematics with the purpose of discovering the world, its organization and surroundings, which was an integral part of human activity in ancient Greece, Babylon, Egypt, India, Persia, China and Rome, philosophers and mathematicians of that times were trying to discover universal formulas for dealing with different mathematical problems. The earliest methods that were used for solving different quadratic equations were geometric. One of the outstanding Greek mathematicians known as Euclid tended to use a number of different geometric methods to solve various quadratic equations. He wrote about his methods and theories in regard to this issue in one of his books called «Elements». Even today this book is considered to be a significant contribution to the development of many branches of mathematics, especially geometry and algebra.

In addition, there were also Indian mathematicians that dedicated a lot of scientific works to the issue of quadratic formulas. One of them, an outstanding Indian mathematician who is known as Brahmagupta, wrote a book where he explained the quadratic formula as a method of solving quadratic equations. The book was published more than two thousand years ago and what is even more surprisingly, it was written completely with words, not with symbols.

A lot of mathematicians far and wide across the world were influenced significantly and inspired by the works and discoveries of scientists that we mentioned above. For example, there was a Persian mathematician, who was influenced by Greeks and Indians, who had achieved a lot in this area by that time, made a great contribution to the development of the problem by suggesting a new way of solution of the quadratic equations. He was the first mathematician who made success by solving this problem in an algebraical way. This way was a serious breakthrough in this area and led to further discoveries that are used even today.

In order to understand better not only the methodology of solving different algebraic problems, but the reasons explaining why it is so important to know and understand all that, it would be logical to have some theoretical background, including knowledge in regard to the history of algebra as a science.

As one of the main branches of mathematics, algebra as a separate science began its own history in the end of the sixteenth century in France. It is one of the broadest branches of mathematics, together with other sciences such as the number theory, analysis and geometry. Generally speaking, algebra is the science dedicated to the study of mathematical symbols and the methods, rules and principles of manipulating these symbols. Algebra is considered to be one of the most important sciences nowadays, it gave birth to numerous discoveries that are applied in various fields of human activities. The origins of the term «algebra» come from Arabic language and can be translated as the reunion of broken parts.

As a matter of fact, algebra in its development went through a number of developmental stages, each of which is characterized by certain achievements and discoveries that followed one another. While in the very beginning of its existence algebra didn’t took a lot of use from the symbolism, it did not last for too long. All in all, there are three major stages in the development of algebra, that can be defined as the following:

• Rhetorical algebra. In terms of this stage, equations are expressed by means of writing in full sentences. This kind of algebra, which was at first used and developed in Babylon, remained the main until the sixteenth century.
• Syncopated algebra. In this stage of development of algebra, some kinds of symbolism were used, although there was no complete set of symbols and their characteristics. For example, there were restrictions of different kinds, such as of usage of subtraction, etc.
• Symbolic algebra is the algebra where the symbolism including all kinds of algebraic symbols are used. The major role in the development of symbolic algebra played Egyptian mathematicians and later, French mathematicians. The symbolic algebra proved the fact that a lot of problems in the area of geometry can be used by means of algebraic methods.

## The conceptual stages of algebra

Apart from the developmental stages, there were also conceptual stages in the history of algebra. There are four stages in terms of concepts of algebra, which are listed below:

• Geometric stage. This concept is characterized by geometric approach and took place in ancient Babylon and Greece.
• Static equation-solving stage. On this stage of conceptual development, the main goal was to find the numbers that could satisfy particular relations. This stage moved algebra away from geometry and gave birth to many ideas that were independent from geometrical concepts.
• Dynamic function stage. In this conceptual stage of algebra, the key motion was the underlying idea. Within this stage, the main role was dedicated to the functions.
• Abstract stage. Within this conceptual stage, the key role is dedicated to the mathematical structure. This kind of algebra was significantly developed in the end in nineteenth and in the twentieth centuries.

The information provided in the article is meant to help students figure out the key moments that have to be payed attention to when dealing with the quadratic formula calculator and other algebraic matters.

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