Using quadratic regression on a graphing calculator, show that the quadratic function that best fits the data on market share in Problem 66 is

f(x) = -0.0117x² + 0.32x + 17.9

Problem 66

The table shows the retail market share of passenger cars from Ford Motor Company as a percentage of the U.S. market.

A mathematical model for this data is given by

f(x) = -0.0117x² + 0.32x + 17.9

where x = 0 corresponds to 1980.

(A) Complete the following table. Round values of f(x) to one decimal place.

(B) Sketch the graph of f and the market share data in the same coordinate system.
(C) Use values of the modeling function f to estimate Ford’s market share in 2025 and in 2028.
(D) Write a brief verbal description of Ford’s market share from 1985 to 2015.

Transcribed Image Text:

Year 1985 1990 1995 2000 2005 2010 2015 Market Share 18.8% 20.0% 20.7% 20.2% 17.4% 16.4% 15.3%