MATH. GRAPHING FUNCTIONS

Math 163 AMP Project

This project is a basic application of some of the key concepts learned during the semester in regards to the graphing of certain useful functions. In particular, it provides a direct link to possible ways mathematics can and may be used in a scientific field. Through the related context and specific questions this project is designed to give you an example of an answer to the question, “when does anyone ever use this stuff?” Enjoy

Suppose an area of low pressure is passing through the United States at noon on a spring day in April, having a shape roughly like a parabola with its vertex at Des Moines Iowa. In addition, as the front stretches across the northern part of the country it resembles a parabola with a vertical shrink factor. See the figure below.

1. Suppose, as seen on the map, a coordinate plane is superimposed on the country with its origin at Des Moines, Iowa. Write the equation for the parabola that would represent the front had a vertical shrink factor of 20.

2. If the front is moving south at 40 mph and retains its initial shape (from #1), what would be the equation of its graph after 4 hours? (Let the units for x and y be in hundreds of miles, so x = -5 is translated as 500 miles west of the Des Moines, and y = 3 is translated as 300 miles north, etc.)

3. Suppose that at midnight (8 hours later) the vertex of the front has moved an additional 250 miles south and 210 miles east of its previous position at 4:00 while maintaining the same shape. (Note that the rate at which the front is moving is no longer needed information.) Write the equation for the parabola that would represent the front at midnight. Remember that the units are in hundreds of miles.

4. a) Draw a graph of the parabola at midnight on the x-y axis keeping Des Moines at the origin and label the locations of Columbus, Memphis, and Louisville on the graph. Be as accurate as you can. State which of these cities the front has passed over and which it has not and explain how you know.

Columbus, Ohio is 550 miles east and 80 miles south of Des Moines;

Memphis, Tennessee is 190 miles east and 430 miles south of Des Moines; and

Louisville, Kentucky is 420 miles east and 230 miles south of Des Moines.

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