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
Follow the Activity procedures:
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