Parameter, variable, and argument I asked a question on English.stackexchange.com but they told me that my question was not about English, and it was rather about math. So, I decided to ask it here :( They closed my thread, so please do not close it here too (I beg you), or at least tell me a website name or somewhere that I can learn :(
What do you call the x in the brackets like that:
f(x) = ax² + bx + c

If I am not mistaken, the x in the brackets is called a variable; a, b, and c are called parameters or variables. Am I right?
The x (or any variable or number) in the brackets can also be called an argument, correct?
But what is a variable in mathematics? For example in the function above, can we call x a variable?
In an equation like:
y = ax² + b + c

x and y are variables (I might be wrong). Is it possible that we can call x and y arguments?
Many thanks
 A: Much like programming, you have functions with parameters. You can call these functions and expect an output.
Lets assume we define a function $f$:
$f: \mathbb Z \to \mathbb Z$
meaning we expect this function to spit out integers when it is fed integers.
Lets furtherly narrow it down, and define the function $g$ as:
$g(x) = x-1$
Now we write x-1, using the parameter x, indicating the $x$ is a placeholder for an unknown value.
Lets try feeding a number to our function. $g(1) = (1)-1 = 0$. Thus, we have input of $1$, and output of $0$. So I wrote a function dependant on a parameter, $x$, a constant, $-1$, and called it with $x=1$ as an argument.
Did that clear things up?
A: Parameter is a variable which is constant with respect to other variables. Like in equation of circle $ x^2+y^2=r^2 $ , $r$ is parameter.
A: A variable is something that can vary, in the context you're interested in.  For $y=ax^2+bx+c$, you could have $x,y$ be variables, with $a,b,c$ constants.  But in another problem you might want to hold $x,y$ constant, and vary $a,b,c$ -- then $a,b,c$ would be the variables.
The term "parameter" has several meanings.  Sometimes we call constants parameters; within a problem $x,y$ are the variables, but between problems we might want to vary $a,b,c$, so they are parameters.  Also, sometimes we call the objects we plug into an $n$-ary function parameters.  For example, when we define $f(x,y)$, we can call $x,y$ parameters to the function $f$.  In short, just about any letter can be called a parameter. :-)
