Question

Please advise on the following:
From 1993 to 2003 the cumulative number N of AIDS cases in thousands can be approximated by,
where corresponds to the year 1993.
N = -2 x2 + 76x + 430, where x = 0 corresponds to.
1) Show how well the equation approximates the data. 2) Rewrite the equation with the right side completely factored.
3)What is the importance onhow this applies to society.

Answer 1

2. N = -2x^2 + 76x + 430.
A*C = -2*430 = -860 = -10*86,
-2x^2 + 86x-10x + 430,
Group the 4 terms into 2 factorable pairs:

(-2x^2+86x) + (-10x+430),
-2x(x-43) + -10(x-43) = 0,
N = (x-43)(-2x-10).