Algebra 2 help: A biologist took a count of the number of migrating geese in a state park and recounted the parks population of geese for each of the next six weeks. Find a quadratic function that models the data shown as a function of x, the number of weeks. Use the model to estimate the number of geese at the lake on week 8.
week; 0 1 2 3 4 5 6
polulation; 762 618 558 582 690 882 1158

Question

Algebra 2 help:  A biologist took a count of the number of migrating geese in a state park and recounted the parks population of geese for each of the next six weeks. Find a quadratic function that models the data shown as a function of x, the number of weeks. Use the model to estimate the number of geese at the lake on week 8.
week;            0       1      2      3       4       5       6
polulation;  762   618   558  582  690  882   1158

agent0smith · Answer

Maybe use the standard form of a parabola,
$$y = ax^2 + bx +c$$
We can find c easily, as that's the y-intercept, or the value when x=0, so c=762. To find a and b, pick two other points... for example (1, 618) and (2, 558) and enter them into the equation along with 762 for c:
$$618= a \times 1^2 + b \times 1 + 762$$
$$558= a \times 2^2 + b \times 2 + 762$$
Now we have two equations which we can solve for a and b.