# Activities

• • • ##### Subject Area

• Math: Geometry: Analytic Geometry

• ##### Author 9-12

60 Minutes

• ##### Device
• TI-92 Plus / Voyage™ 200
• ##### Other Materials
This is Activity 9 from the EXPLORATIONS Book:
Discovering Math on the Voyage 200.

## Graphing an Extra Dimension

#### Activity Overview

In this activity, students learn to graph equations in 3-D space called surface. They learn to use graphs in 3-D. They will focus on the characteristics of surface types called paraboloids.

#### Before the Activity

• See the attached PDF file for detailed instructions for this activity.
• Print pages 67 - 72 from the attached PDF file for your class.
• #### During the Activity

Distribute the pages to the class.

• Examine how the value of a affects the graph of
y = a x2
• Enter various values of a and graph the function
• Note the observations in a chart

• Examine how the constants a and b affect the graph of the equation z = a x2 + by2
• Enter a = 1 and b = 1 and graph the function
• Observe the resultant graph of z = x2 + y2 is a 3-dimensional parabolic curve
• Trace the surfaces of the graph in the xy, xz, and yz planes
• For other values (both positive and negative) of the constants a and b, predict changes in the parabolic curve
• Graph the function for the other values of a and b
• Compare the observed effect with the predicted effect
• #### After the Activity

Review student results:

• As a class, discuss questions that appeared to be more challenging
• Re-teach concepts as necessary