Question

the number of cases of a new disease can be modeled by the quadratic regression equation $y=-2x^{2}+40x+8$, where $x$ represents the year.
which is the best prediction for the number of new cases in year 15?
a. 72
b. 276
c. 158
d. 394

Explanation:

Step1: Substitute x=15 into equation

$y=-2(15)^2 + 40(15) + 8$

Step2: Calculate squared term

$15^2=225$, so $-2\times225=-450$

Step3: Calculate linear term

$40\times15=600$

Step4: Sum all terms

$y=-450 + 600 + 8$

Answer:

A. 72