Exploring Parabolas

Activity I

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 following equations are displayed on the the green graph:

  • y = x^2 - b * x + a
  • y = -x^2 + 5 * x - 6
  • y = x^2 - 14 * x + 48
  • y = x^2 + 14 * x + 48
  • y = x^2 + x - 2
  • -x^2 + 11 * x - 28
  • -x^2 - 8 * x - 15

Match the correct quadratic equation to the matching parabola.

yellow line parabola  
green line parabola  
red line parabola  
pink line parabola  
black line parabola  
blue line parabola  
light blue line parabola  

As you are matching the graphs to the equations, the following questions may help prompt your thinking.

Questions:

  1. Can you identify the roots of the equation based on the graph?
  2. Can you write the equation in factored form?
  3. What's the sum of the roots?
  4. What's the product of the roots?
  5. Can you write the equation in expanded form?

Once you have matched the equations to the corresponding graphs, your next task is to find the coordinates on the blue graph that control the location of any of the given parabolas.

Questions:

  1. What coordinates (a, b) can you find that move the black parabola to the position of one of the other parabolas?
  2. How many coordinates can you identify of the 6 graphs?

Activity II

Open the second 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.

Questions:

  1. What coordinates (a, b) can you find that move the dark grey parabola to the position of one of the other parabolas?
  2. How many coordinates can you identify of the 6 graphs?

Assessment:

Generalize what you observed as you worked with the equations, the factored form, the roots, the graphs, and the coordinates (a, b).

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