Parametric Equations and Graphing Techniques

This video tutorial demonstrates how to graph parametric equations using a TI-83 or TI-84 calculator. It covers setting the calculator to parametric mode, graphing various examples, and adjusting the window settings for different intervals. The video includes examples of linear, trigonometric, and complex curves, providing step-by-step instructions for each. It also explains how to use the trace and table features to analyze the graphs.

What is the first step to graph parametric equations on a TI-83/84 calculator?

• Enter the equations directly

• Set the calculator to parametric mode

• Use the trace feature

• Adjust the window settings

In the first example, what is the equation for y?

• y = 5 + t

• y = t^2

• y = 2t

• y = 4 - t

Why is it important to set a tstep value when graphing parametric equations?

• To change the color of the graph

• To make the graph appear larger

• To adjust the calculator's brightness

• To ensure the graph is smooth

What feature can be used to find specific points on the graph?

• Graph

• Trace

• Zoom

• Mode

In the second example, what is the interval for T?

• 0 to Infinity

• -5 to 5

• 0 to 10

• -10 to 10

What shape does the graph form in the third example with x = 5 sin T and y = 2 cos T?

• Line

• Parabola

• Ellipse

• Circle

How is the asteroid-shaped curve traced as T increases?

• Horizontally

• Vertically

• Counterclockwise

• Clockwise

What is the major axis length of the ellipse in the third example?

• 4 units

• 12 units

• 6 units

• 10 units

In the final example, what is the equation for x?

• x = 2 sin T

• x = 5 sin T

• x = 4 cos T

• x = 6 cos T

What is the purpose of using the table feature on the calculator?

• To adjust the calculator's brightness

• To find specific points to plot

• To zoom in on the graph

• To change the graph's color