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
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.