Education Technology

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.

    Follow the Activity procedures:

  • 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