Exploring Roots of a Quadratic Equation

Activity

Open the Java Applet.

Note: The Java applet will open in a separate window. Arrange your browser windows so that the applet and the student page can be easily viewed.

The Java Applet displays two graphs. We'll refer to the graph on the left as the blue graph and the graph on the right as the green graph. The blue graph can be manipulated. The green graph's display depends on the changes made on the blue graph.

  1. Experiment with different values of a and b using the arrows above and to the right of the blue graph.
    What happens on the green graph?
    • Does the black parabola move?
    • Does the red parabola move?
    Can you control the movement?
  2. Click at various places on the blue graph.
    What happens on the green graph? Can you control the movement? For example, can you predict where the red parabola will be if you click on different points for a and b? Try:
    • (1, -2)
    • (-3, 10)
    • (9, -9)
    • (0, 0)
  3. CHALLENGE: Move the red parabola so that it is in the same position on the graph as the black parabola.
    What are the coordinates of the point on the blue graph?

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