Family Features I - Task
Each of the three figures presents a family of quadratic functions.
In each family f(x) = ax² + bx + c the sum of the coefficients is 7, meaning a+b+c=7.
In each family the coefficients are varied by a different method.
- What are the common properties to all the graphs in each family?
- What are the common properties to the graphs in all three families?
- Construct other families of quadratic functions in polynomial form, in which the coefficients change in a systematic way. Describe the interesting phenomena you observe.
- Which of these phenomena can you explain?
- Describe conclusions, conjectures, and questions that arose.