You will use the following situation to complete your task :

A diver performs a swan dive. The path of the dive can be described by the following equation: y = (–1/2) x ² + 2 x + 10. All measurements are in feet. The variable y represents the distance from the surface of the water. The variable x represents the distance from the side of the pool. For ease of calculation, assume that the end of the diving board and the side of the pool are located at the same point.

Task:

A diver performs a swan dive. The path of the dive can be described by the following equation: y = (–1/2)x ² + 2x + 10. All measurements are in feet. The variable y represents the distance from the surface of the water. The variable x represents the distance from the side of the pool. For ease of calculation, assume that the end of the diving board and the side of the pool are located at the same point.

Task:

1. Use the above situation to complete parts A1 through A7:

1. Find the x- and y-intercepts and vertex algebraically, showing all work.
2. Graph the equation with appropriate labels.
3. Identify which point corresponds to the following:
   • The point at which the diver enters the water
   • The height of the diving board
   • The highest point in the dive
4. Determine the height/depth of the diver when the diver is 8 feet from the side of the pool.
5. Determine whether the algebraic and graphical work correspond.

1. Explain whether one aspect helps clarify the other.

6. Determine which quadrants of the graph are relevant to this problem.

1. Explain whether there were algebraic answers that were not reasonable solutions for this problem.

7. Discuss whether it is possible for an algebraic solution to be mathematically correct but not applicable to a given situation.

1. Describe a situation where this solution might occur.

Price: $9.45

Solution: The downloadable solution consists of 4 pages, 545 words and 1 charts.
Deliverable: Word Document