What are the Differences Between a Linear Equation and a Quadratic Equation?

Article Summary: Math textbooks are loaded with a lot of terms. But unlike other subjects, math terms are not always easy to understand based on their name alone. Many students learn dozens of mathematical skills without actually learning the use of the skill or even the name of the skill.

Math textbooks are loaded with a lot of terms. But unlike other subjects, math terms are not always easy to understand based on their name alone. American literature is pretty self explanatory. Trigonometry, well, that may need a little explaining! One common term that appears often is "equations." For many, this is a buzz word that is recognizable as a math term but truly understanding the term may sometime escape people.

Equations. We hear that word all the time when it comes to the study of math, but like many math terms we may not be clear on their meaning. One of the reasons for this is that there is more than one kind of equation and this can create some confusion. The two most common equations are linear equations and quadratic equations but, of course, merely giving an equation a name does not necessarily explain what it is. So, a clearer definition of what exactly the two most common equations - linear and quadratic equations - is needed.

On a baseline level, a linear equation refers to a particular equation that is graphed on a straight line. Additionally, a linear equation possesses on the line one variable that is commonly referred to as "X" and "X" will always be of a degree that is 1 at most. (That is, there are no exponents; but if you are looking for exponents then be patient because we will get to them shortly!) A common example of a linear equation would be 1x + 2 = 3. Clearly, x would equal 1 in this particular example and it can be figured out by merely using a little algebra on the equation to figure out X. 3 minus 2 equals 1. Therefore, X must equal one as 1 x 1 equals one. And, nope, not all linear equations are that easy as they come as complex as 6(x + 3) = 24 (x +0), but the common factor of isolating x to find the answer doesn't change.

A quadratic equation is only different from a linear equation in one respect: one or more of the figures is squared. (The word quadratic derives from the Latin word for squared) The common form of a quadratic equation is ax2 + bx + c = 11. In such a equation, if a = 1, b = 2 and c = 3 then X must equal 2. We know this because 2 squared is 4 and 4 x 1 = 4. 2 x 2 = 4. As with a linear equation, there can be more complicated versions of a quadratic equation but just with the simple and complex linear equations basic algebraic operations can yield the correct answer.

Ok, we know the difference between the two. But what is the overall value of learning this aspect of algebra?

Of course, you have probably noticed that the common denominator (well, there's a mathematical term!) is the presence of a variable. This is also the most important element found in algebra because it allows math to move forward when all the information needed to come to an answer isn't available. This is very important because if the ability to figure out problems and equations without and figuring around variables then the ability to study math would be finite. Now, if the ability to study math was finite while math itself was infinite then the ability to understand and use mathematical skills would be limited. This would have an incredibly negative impact on a number of fields that require a deep understanding of math such as engineering, astronomy and even architecture.