What is the difference between a parameter and a variable ? What role do parameters and variables have in a family of functions ?

Defined and explained in the explanation section

Step-by-step explanation:

A) Difference between a variable and a parameter is that;

A variable is simply the way in which an attribute or quantity is represented while a parameter is normally a constant value or symbol in an equation that describes a model.

B) In a family of a function like a quadratic function of say:

f(x) = ax² + bx + c.

In this example, the variable is x which is the input to the function while the symbols a, b, and c are the parameters which determine the behavior of the function f. Thus, for each value of the parameters a, b, c, we will obtain a different function.