Question

finding and using a quadratic regression model
a new hospital tracked the number of births during its first 6 months of operation, as shown in the table.
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.
month number of births
1 137
2 110
3 93
4 70
5 65
6 77
feedback
input the values in the table into the regression calculator and choose “quadratic regression.” once you find the model, use the equation to extrapolate the data.

Explanation:

Step1: Use regression calculator

Input (1, 137), (2, 110), (3, 93), (4, 70), (5, 65), (6, 77) into a regression - calculator and select quadratic regression.

Step2: Get quadratic function

The calculator gives $a\approx - 4$, $b\approx - 10$, $c\approx151$, so $f(x)= - 4x^{2}-10x + 151$.

Step3: Predict for month 8

Substitute $x = 8$ into $f(x)$: $f(8)=-4\times8^{2}-10\times8 + 151=-4\times64-80 + 151=-256-80 + 151 = 103$.

Answer:

$f(x)= - 4x^{2}-10x + 151$; $103$