In algebra, a variable is usually a letter or other symbol that stands for a number or quantity that may vary. Variables can also be used to represent functions as well as quantities in other mathematical disciplines. The most commonly used variable in algebra is "x." Below is an example of a simple algebraic equation.

x + 2 = 4

In the above equation, x is equal to 2. We know this because 2 + 2 = 4, and in this case x can only take on one value. Variables are used in many different ways, and one of the reasons they can be particularly useful is because they make it possible to solve a range of different problems using just one computation. One such example (there are many) is the quadratic formula, which can be used to solve any quadratic equation:

The variables a, b, and c can more specifically be referred to as parameters. They are variables in that they can take on many different values, but when using the quadratic formula, a, b, and c are known values taken from a specific quadratic equation that when plugged into the formula, computes the unknown variable, x.

Types of variables

Like in the example of the quadratic formula above, variables commonly take on different roles within an equation. There are more different types of variables, but the list below includes some of the more commonly used types of variables in algebra. Using the general form of a quadratic equation as a reference:

Variables in functions

When variables are discussed in the context of functions, they are the argument, or input of the function. For example, in the function

f(x) = x + 3

x is the argument of the function, since the output of the function is based on some variable output of x:

f(3) = 3 + 3 = 6

f(-2) = -2 + 3 = 1

f(⅓) = ⅓ + 3 = 3⅓

In the above function, 3 is a constant, since it does not change based on the value of x. This 3 is an example of a constant that would not be considered a variable, as discussed above.