Application of Quadratics

Name: Class: Date: #

Home Run Ball: Fenway Park, the home ballpark of the Boston Red Sox, is one of the most famous and most recognized professional sports venues in the United States. Built in 1912, Fenway Park is revered for its history and for the generations of ball players that have played on its field. The ballpark is also known for its unique outfield wall, labeled the Green Monster, which stands 37-feet high and is an imposing structure for batters. The image below shows the dimensions of the park. The numbers in white represent the distance between home plate and the outfield wall.

The Green Monster, due to its immense height, has prevented many well-struck baseballs from becoming home runs. Your task is to model the flight of a home run ball at Fenway Park. The table above displays information about heights of the outfield falls at Fenway Park that you can use to construct your model.

Home Plate Assignment:

. Formulate a model for the flight of a home run ball at Fenway Park . State the model’s assumptions . Describe the position of the baseball when it reaches its maximum height . Determine the max distance that the baseball would travel if not impeded . Create a graph showing the path of the baseball . Explain why your model corresponds to a home run ball at Fenway Park

Historic Hotels: You and your team work as financial consultants. Your primary function is to provide clients financial advice. You have a client who just inherited a historic hotel in Boston, Massachusetts. Your client’s situation is described below.

Ms. Amanda Graham has just inherited a historic hotel. She would like to keep the hotel but she has little experience in hotel management. The hotel has 80 rooms. The previous owner told Ms. Graham that all of the rooms are occupied when the daily rate is $180 per room. The previous owner also stated that the number of occupied rooms depends on the daily rate. For every 5$ increase in the daily rate, one fewer room is occupied. Also, there is a $4 daily cost for maintaining and servicing each occupied room.

Ms. Graham would like to know what the daily rate should be in order to maximize the daily profit.

Assignment

 Formulate a mathematical model to solve this problem  State the model’s assumptions  Determine the daily rate that will maximize her daily profit  Justify the solution using a table or graph  Discuss the model’s limitations