Exploring Parabolas

Activity I

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).

 Math Forum Resources Applications of Parabolas How are parabolas used in real life? Describing the Graph of an Equation Which of the following is true of the graph of the equation: y = 2x^2 - 5x + 3? Equation for an Arch I am trying to draw an arch that will go in the ceiling of a building. The arch will be at a maximum height of 28 inches... Graphing Parabolas How do you know how to graph a parabola from looking at its equation?