A biologist took a count of the number of migrating waterfowl at a particular lake, and the lake’s population of waterfowl on each of the next six weeks. Find a quadratic function that models the data as a function of x, the number of weeks. Use the model to estimate the number of waterfowl at the lake on week 10. week 0 1 2 3 4 Population 585 582 629 726 873

Quadratic function ( in standard form ):

y = a x² + b x + c

x = 0:

635 = 0 + 0 + c

c = 635

x = 1:

644 = a + b + 635

a + b = 9

x = 2:

719 = 4 a + 2 b + 635

4 a + 2 b = 84

and now we have a system:

a + b = 9 / * ( - 2 )

4 a + 2 b = 84

- 2 a + 2 b = - 18

+

4 a + 2 b = 84

2 a = 66

a = 33; b = - 24;

Function is:

f ( x ) = 33 x² - 24 x + 635

f ( 8 ) = 33 * 64 - 24 * 8 + 635 = 2,112 - 192 + 635 = 2,555

The number of waterfowl on week 8 would be 2,

Step-by-step explanation: