Equations for Curves Passing through a Given Set of Points

Published on
07/20/2005

Activity Overview

In this Derive™ activity, students explore equations of curves which pass through a set of given points. They use this method to determine the location of a distribution center which is equidistant from the outlets of a large department store chain.

Before the Activity

See the attached DFW file for detailed instructions for this activity

Print pages from the attached DFW file for your class

During the Activity

Distribute the pages to the class.

Follow the Activity Procedures:

Set up a 2D plot window

Use 3 random locations on the coordinate system

Simplify the expression and assign result to the variable loc

Guess the best location for the center of a circle which encompasses the 3 points

Substitute guesses for the center and radius of the circle in the equation for the center of a circle and plot the result

Expand the equation of the circle

Simplify the given expression to see the three unknown equations

Solve for the radius, and the coordinates of the center

Extend the procedure to find a curve that passes through a given number of points by considering the equation for a parabola

Generate three points at random and assign the result to a variable

Plot the three points

Substitute these three points into the equation of the parabola to obtain three equations in the three unknowns

Solve the equations for the unknowns and plot the parabola

After the Activity

Students answer questions listed on the activity sheet.

Review student results:

As a class, discuss questions that appeared to be more challenging