The number (in thousands) of new, privately owned housing units completed in the United States is shown in the table. Here x represents the number of years since 2006, and y represents total housing units completed.

(a) Use the ordered pairs (x, y) to make a scatter diagram of the data.

(b) Would a linear or a quadratic function better model the data?

(c) Should the coefficient a of x² in a quadratic model y = ax² + bx + c be positive or negative?

(d) Use the ordered pairs (0, 1980), (4, 650), and (8, 880) to find a quadratic function that models the data.

(e) Use the model from part (d) to approximate the number of such housing units (in thousands) completed in 2008 and 2012. How well does the model approximate the actual data from the table?

Transcribed Image Text:

Year 2006 2008 2010 2012 2014 2016 0 2 4 6 8 10 y 1980 1120 650 650 880 1060 Data from U.S. Census Bureau.