Complicated function

Question

The number of households f(x),  in millions. participating in the Food Stamp Program from
1999 to 2004 (where x = number of years) is represented by the function
f(x) = 0.78x^2 -5.5x+12.68
a. During which years would the number of households be less than six million?
b. In which year was the number of households participating at a minimum

c. How many households received food stamps that year

Answer 1

I plotted the graph of the function and obtained:

The first column is the year number or x, the second column is the number of households.

1    7.96  1999
2    4.8    2000
3    3.2    2001
4    3.16  2002
5    4.68  2003
6    7.76  2004

Then my answers will be:

a. During which years would the number of households be less than six million? 2000, 2001, 2002, 2003

b. In which year was the number of households participating at a minimum? I will answer 2002

c. How many households received food stamps that year? 3.16 millions of households.

 

Answer 2

Plugging into quadratic formula:

A is .78 b is -5.5 and c is 12.68-6

X is 5.4 and 1.6 

 

Differentiring gets 1.56x-5.5

Setting this to zero we get 3.52

 

Plug this in to find number of households on food stamps in millions.

 

Hooe that helps,

Deanna