The total amount spent by some number of people on clothing and footwear in the

Question

The total amount spent by some number of people on clothing and footwear in the years 2000-2009 can be modeled by the quadratic function f(x) = -4.069x^2 + 71.85x + 96.37, where x = 0 represents 2000, x = 1 represents 2001, and so on, and f(x) is in billions of dollars. Since the coefficient of x^2 in the model is negative, the graph of this quadratic function is a parabola that opens down. Will the y-value of the vertex of the graph be a maximum or a minimum? According to the model, in what year during this period was the amount spent on clothing and footwear a maximum? The y-value of the vertex of the graph will be a because a parabola which opens down has a

Explanation / Answer

a) As it is downward facing parabola, vertex would give maximum value.

b) Maximum ,: find vertex

x = - (71.85/2*-4.069) = 8.82

Year = 2009

c) y value of vertex is given f(8.82) = -4.0698.82^2 + 71.85*8.82 + 96.37 = 413.55

It has a maximum

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