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Quadratic Functions

Author:mmteresasssblm
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]? Do the following activities and then answer the questions.

  • 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. 

  • 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?

  • 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?

  • 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?

  • 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?

Write your full name and your grade.

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