Addition of functions: the Polynomial Form Family features I Each of the three figures below presents a family of quadratic functions. In each family, the sum of the coefficients of the correspondence rules f(x) = ax² + bx + c defining the functions is 7 (a+b+c=7). In each family the coefficients are varied by a different method. What are the common features to all the graphs in each family? What are the common features 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. f1 f2 f3 f4 f5 f1 f2 f3 f4 f5 f1 f2 f3 f4 f5

The three components Quadratic functions - polynomial form Addition of functions Polynomials Constructing a function in Polynomial Form Changing a coefficient Family features I Family features II Sum of linear and quadratic Sum of quadratic functions Green areas Constructing quadratic functions through points Extension: polynomials Exercise 1 Exercise 2 Exercise 3 Exercise 4 Exercise 5 Exercise 6