The amount of background noise is important to television news reporters. One station developed the formula
N = -r^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.
T=4 then N=86
T=5 then N=89
T=6 then N=90
T=7 then N=89
T=8 then N=86
We see that N is maximum when t=6
Answer: 6 seconds
OR.....
The maximum will be at the vertex of the graph. You can get the t coordinate by taking:
-b/2a
= -12/(2*-1)
= -12/-2
= 6
The max is at 6 seconds.