Parameter

A parameter (Greek παρά para, German 'neben' and μέτρον metron 'measure'), also a form variable, is a variable in mathematics that occurs together with other variables but is of a different quality. One also speaks of a parameter being arbitrary but fixed. It thus differs from a constant in that the parameter is only constant for a case currently under consideration, but can be varied for the next case.

In the equation $y=b\cdot x^{2}$ both and are variables. Depending on whether or is considered as a parameter, $y=b\cdot x^{2}$ then describes a function of the other variables, each with a different character:

Keeping fixed gives a quadratic function with $y=f\left(x\right)=b\cdot x^{2}$ whose graph is a parabola with opening This opening depends on the particular choice of the parameter
Keeping fixed gives a linear function with $y=f\left(b\right)=x^{2}\cdot b$ whose graph is a straight line with slope $m=x^{2}$ through the origin of the y-b plane. The slope depends on the particular choice of the parameter

If you set different values for a parameter one after the other, you get a set of curves.

For example, a parameter can influence the graph of a function with y=f(x) various ways:

$y=f\left(x\right)+p$ : A change of the parameter compared to leads to a shift of the graph in the direction of the y-axis by units.
$y=f\left(x+p\right)$ : A change of the parameter compared to leads to a shift of the graph in the direction of the x-axis by units.
$y=p\cdot f(x)$ A change of the parameter compared to leads to stretching or compression in the direction of the y-axis. If the amount of is less than 1, then there is compression. If negative, then the graph is also mirrored on the x-axis.
$y=f(p\cdot x)$ : A change of the parameter compared to leads to stretching or compression in the direction of the x-axis. If the amount of is less than 1, then there is stretching. If negative, then the graph is also mirrored on the y-axis.

For another use of the term parameter in mathematics, see parameter representation.

By convention, parameters are usually designated with letters from the beginning of the Latin or Greek alphabet ( $a,b,c,\dotsc$ or with indices $a_{1},a_{2},a_{3},\dotsc$ or α $\alpha ,\beta ,\gamma ,\dotsc$ etc.).), but variables with letters from the end of the alphabet ( $x,y,z;x_{1},x_{2},\dotsc ;\xi _{1},\xi _{2},\dotsc$ ).

Parameter

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