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GeoGebra

The parabola in vertex form

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We start from a real function; of a real variable, f(x)=a(x-h)^2+k, where a, h and k are parameters. How does the function change when these parameters vary in the interval [-5;5]? Do the following activities and then answer the questions.

  • Keep Fixed the values a=1, h=0, and k=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 h and k. Then, vary a. How does the graph of the function change according to the variation of a?

  • Keep fixed the values a and k. Then, vary h. How does the graph of the function change according to the variation of h?

  • Keep fixed the values a and h. Then, vary k. How does the graph of the function change according to the variation of h?

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