Method 1: If you know how each of the parameters affects the parent function, y = x², then you can use that knowledge to find a model to fit your data. This method is like a game . . . so have fun with this!

For a quick review of the parameter changes, check out these sites!

• To review how the parameters affect a quadratic function in standard form, y = ax² + bx + c, use the sliders in the applet below to investigate how a, b, and c affect the graph.

Quadratic Function Applet

• To review how the parameters affect a quadratic function in vertex form, y = a(x - h)² + k, use the sliders in the applet below to investigate how a, h, and k affect the graph.

Transformations on a Parabola Applet

Now that you have become an expert at how the parameters affect the parent function, y = x², record a summary of your findings using your notes.

Now that you have spent a few minutes experimenting and reviewing the effects of the parameters on the parent function, y = x², let’s have some real fun! At each of the sites below, the graph of the parent function, y = x², will be shown in RED and another quadratic function will be shown in BLUE. Your challenge for each will be to apply your knowledge of the parameters and transform the RED parabola to coincide with the BLUE parabola!

Go to this page and you will see:

Click on “View Online (free)” and you will see the RED parabola and the BLUE parabola! Let the challenge begin! See how quickly you can get the two to coincide!

Now go to this page and try another! It might be fun to challenge a friend to see who can match the parabolas in the fewest number of moves!