defines a family of quadratic functions: each choice
of values for parameters a, b, c, d, e produces a different quadratic function.
The family is represented in the dynamic figure below
(which is a special case of the Parametric Families tool).
By leaving some of the parameters fixed and changing some others, you obtain a
family of functions that is a sub-family of the original family.
You can construct many families in this way.
Produce: -
Sub-families generated by keeping four of the parameters fixed and changing one.
- Sub-families generated by keeping three of the parameters fixed and changing two.
- Conitnue reducing the number of fixed parameters and increasing the number of those that change.
Choose a family that looks interesting to you.
Describe the family you have chosen: What properties are common
to all the functions in the family? What properties vary?
Write correspondence rules for several functions in the family you have chosen.
Write a general expression for your family, using only one parameter.
Explain the reasons behind the special properties of the family of functions you have chosen.
