# 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

**determines whether it is a valley or mountain parabola and how sharp is the scaling of the parabola.**

*a*## 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,

**and**

*a***in the equation**

*b**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.

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