Exploring Parameters of Polynomials

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Use the applet below in order to work on the following tasks: Task 1 Change the parameter value a by moving the point on the slider with the mouse. 
  • How does this influence the graph of the polynomial? 
  • What happens to the graph when the parameter value is (a) greater than 1, (b) between 0 and 1, or (c) negative?
  • Write down your observations.
Task 2 Change the parameter value b. How does this influence the graph of the polynomial? Task 3 Create a slider for a new parameter c and enter the quadratic polynomial f(x) = a * x^2 + b x + c. Then, change the parameter values b and c and find out how this influences the graph of the new polynomial.
– GeoGebra Materials Team, Judith Hohenwarter

Information: Exploring Parameters of Polynomials