Question

The bar graph shows the number of Asturian households, in thousands, living in poverty from 1999 to 2004. The table holds a quadratic function for the data, where y is the number of households, in thousand living in poverty × years after 1999. 10. 10 1999 2000 2001 2002 2003 2004 QuadReg y = ax2 + bx + c a = 0.2299729818 b = - 0.4599459636 c = 7.5426446323 a. Use the table to express the model in function notation, with numbers rounded to two decimal places #(x) = 0.23x2 + - 0.46x + 7.54 b. According to the function in part (a), in which year was the number of households living in poverty at a minimum? 2000 (Round to the nearest year as needed.) c. Use the model to find the number of households, in thousands, for that year. 7400 (Round to one decimal place as needed.)

Answer 1

a. The quadratic function for the data can be expressed in function notation as follows, rounding the coefficients to two decimal places:

#(x) = 0.23x^2 - 0.46x + 7.54

b. To find the year when the number of households living in poverty was at a minimum, we need to find the vertex of the parabola given by the quadratic function. The x-coordinate of the vertex is given by:

x = -b/(2a)

Substituting the values for a and b given in the problem, we get:

x = -(-0.4599459636)/(2*0.2299729818) ≈ 1

This means that the minimum occurs one year after 1999, i.e., in the year 2000.

c. To find the number of households living in poverty in the year 2000, we can substitute x = 1 in the function:

#(1) = 0.23(1)^2 - 0.46(1) + 7.54 ≈ 7.4

This means that there were about 7,400 households living in poverty in Asturias in the year 2000.

Explanation: