nekiwa07 wrote:

The number of passengers on a certain bus at any given time is given by the equation P = –2(S – 4)^2 + 32, where P is the number of passengers and S is the number of stops the bus has made since beginning its route. If the bus begins its route with no passengers, what is the value of S when the bus has its greatest number of passengers?

a) 9

b) 6

c) 4

d) 2

e) 1

\(P = –2(S – 4)^2 + 32\):

\(–2(S – 4)^2 = (-2)*(square \ of \ a \ number)= (negative)*(non-negative) = (non-positive)\). So, this term is negative or 0.

Therefore, P, the number of passengers, will be maximized when \(–2(S – 4)^2\) is 0. In this case \(P_{max} = –2(S – 4)^2 + 32= 0+32=32\). For, \(–2(S – 4)^2\) to be 0, S should be 4.

Answer: C.

Hope it's clear.