Mathematics

Grade Levels: 6th Grade, 7th Grade, 8th Grade, 9th Grade,

Topics: AlgebraCoordinate SystemsExpressions and Equations

Common Core State Standard: F-IF.7e,

Knowledge and Skills:

• Can evaluate expressions by substituting values for variables

• Can simplify expressions using correct order of operations

• Can plot a point in a two-dimensional coordinate system, given the coordinates, or determine the coordinates of a given point

Lesson:

If the Space Shuttle were to make a maintenance trip out to a satellite in geosynchronous orbit, the Shuttle would need to enter into an elliptical orbit around the earth. That orbit could be described by this equation:

where a and b are numbers that determine the shape of the ellipse.

If all distances are measured in thousands of miles, then an actual orbit might be described by this equation:

1. Find the value of y for each value of x (to two decimal places):

2. Plot the ordered pairs from the table above and sketch the curve that

connects them.

3. In this orbit, the Earth would be at the position (-12.5,0), and the satellite

would be at the position (13.5,0). Plot these points on your graph. How far is

the earth from the satellite?

**Answers:**

1.

2.

3.

26,000 miles