Question

A new hospital tracked the number of births during its first 6 months of operation, as shown in the table.

A 2-column table with 6 rows. The first column is labeled month with entries 1, 2, 3, 4, 5, 6. The second column is labeled number of births with entries 137, 110, 93, 70, 65, 77.
Find a quadratic function that models the data. Round numerical values to the nearest whole number.

f(x) =
x2 +
x +



Use the function to predict the number of births for month 8. There will be about
births.

Answer 1

A least-squares quadratic fit gives approximately
f(x) = 4.34x^2 − 43.46x + 178.30.
Rounding coefficients to the nearest whole number (as requested) yields

f(x) = 4x^2 − 43x + 178.

Using this rounded model for month 8:
f(8) = 4(8)^2 − 43(8) + 178 = 90.

There will be about 90 births.