We start from a real function; of a real variable, f(x)=ax^2+bx+c, where a, b and c are parameters. How does the function change when these parameters vary in the interval [-4;4]? [br]Do the following activities and then answer the questions.
[list][*]Keep Fixed the values a=1, b=0, and c=0. Then, observe the graph of this function. Identify the vertex of the parabola, the x-intercept, and the y-intercept. [/*][/list]
[list][*]Keep fixed the values b=0 and c=0. Then, vary a. How does the graph of f(x) =ax^2+bx+c change according to the variation of a?[/*][/list]
[list][*]Keep fixed the values of a=1 and b=0, and make c vary. How does the graph of f(x) =ax^2+bx+c change according to the variation of c?[/*][/list]
[list][*]Keep fixed the values of a=1 and c=0, and make b vary. How does the graph of f(x) =ax^2+bx+c change according to the variation of b?[/*][/list]
[list][*]Now, vary all the values of a, b, and c. How does the graph of the function change according to the variation of a, b, and c?[/*][/list]
Write your full name and your grade.