Addition of functions: the Polynomial Form Family features II The figures below present two families of quadratic functions. In each family the coefficients are varied in a systematic way. Note that the functions in each family have a common axis of symmetry. Investigate other familes of functions that are formed by changing the coefficents. Find other examples of families in which all the functions have a common axis of symmetry. Which of the phenomena can you explain? Describe conclusions, conjectures, and questions that arose. 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