Use the data from Exercise and use quadratic regression to find a function g that models these data.
(a) Give the function.
(b) Graph the function with the data points.
(c) Find the estimated number of violent crimes with this model for the year 2012.
Exercise
According the U.S. Department of Justice, the following table gives the number (in thousands) of violent crimes committed in the given years.
Table
Year | Crimes |
2004 | 1360 |
2005 | 1391 |
2006 | 1418 |
2007 | 1408 |
2008 | 1393 |
2009 | 1326 |
2010 | 1246 |
(a) Let x = 4 correspond to the year 2004. Find a quadratic function f(x) = a(x − h)2 + k that models these data using (6, 1418) as the vertex and the data for 2009.
(b) Estimate the number of violent crimes in 2012.
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