We are studying linear and quadratic functions and the problem is stated as: "The Political Noise Problem. The amount of background noise is important to television news reporters. One station developed the formula N=-t^2+12t+54 showing the noise level in decibels (N) as it relates to the time after the speaker stops talking in seconds (t). How many seconds after the speaker stops will the noise level be the greatest? Write and tell how you decided."
In calculus, this is easy. In algebra, a bit more complicated.
write the equation in the form of
N=a(t-h)^2 + k
h will tell you when N is max (or min), then t-h. If a is negative, as it will be here, N is max when t=h. When a is +, it will be a minimum.