# Which is a parameter?

## Understanding and function of the parameter

A parameter is a constant to be determined, an indefinite . So in the equation ƒ(x) = ax + 3, a is the parameter, the indefinite one, and x is the variable.

The terms parameter and variable are often – completely wrongly – used interchangeably. Just like a variable, the parameter can take on different values and can therefore vary, does not mean that both may and can be equated. A pony and a horse also have many similar characteristics, but that does not make a horse a pony and vice versa.

In addition, the parameter and the variable, certainly within a function, do not fulfill the same role. This is apparent, for example, when differentiating or primitive. You differentiate a function by the independent variable(s) and not by the parameter(s), although that is of course possible.

## Variable

The variable in an equation determines the type of that equation. In the equation ƒ ( x ) = ax + 3, the variable, x in this case, determines that the relationship is linear ; whether the type is linear. For example, the equation ƒ(x) = ax^2+bx+c is of type quadratic (or parabolic) .

## Parameter

With a parameter you adjust the ' behaviour ' within a type of comparison. In the case of the equation ƒ ( x ) = ax + 3 you can determine with the parameter a whether the equation is increasing or decreasing and how 'hard'. In the case of the quadratic type , the a determines whether it is a valley or mountain parabola and how sharp is the scaling of the parabola.

## Parameters as “stand in”

As soon as a parameter is given a value, the parameter changes to a coefficient, base, power or constant: depending on the type of equation and position of the parameter . As long as the parameter has no value it is a 'stand-in' for eg the coefficient etc. just like a 'stuntman' is for an actor.

Gets the parameter a `eg. the value 5 in the equation ƒ ( x ) = ax + 3 ( 5x + 3) then '5' is the slope of the line and 3 is the constant or initial value. By analogy with the foregoing, a and b in the equation ƒ(x) = ax^2+bx+c are also coefficients and c is the constant.

## From parameter to parameter representation

In line with the foregoing, considering the term parametric representations for a curve or equation of motion is not only desirable, above all necessary. The concept of parametric representation is confusing and, moreover, insignificant. (The examples that are used are taken from Getal & Ruimte VWO Mathematics B part 3 digital edition). The choice for this is unconscious and could also have come from a site such as Math4all.nl ).

The equation in figure 1 (p.161) is called parametric representation just like in figure 2 (p.162) and it is very confusing and inconsistent. If some consistency in name or reasoning would have been taken into account, then the name for figure 2 'parameter-parameter representation' would cover the load better; a , b , and are parameters here .

In figure 3 (p.171) the concepts of uniform circular motion and harmonic vibration are suddenly introduced instead of parametric representation. Foreign! Finally, insofar as the confusion is not yet complete, the list of terms is supplemented with the term equation of motion , see figure 4 (p. 172). Is a uniform circular motion different from a motion ? No , it's a special case.

## Equation of motion instead of parametric equation

In order to create unambiguity, but above all clarity, it is my recommendation to delete the concept of parametric representation and replace it with equation of motion . The concept of equation of motion is an equation that represents the motion of a point. That movement can be uniform, but also accelerated, harmonic and the equation may or may not be provided with parameters , as with an equation.