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math

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Could someone help explain what I am to do?
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?
I believe that I would need to figure out the vertex of the numbers but I am confused as how I would do that. Is their a formula?

  • math -

    Are you doing pre-calculus or calculus?

    In calculus, the maximum is obtained by setting
    f'(t)=derivative with respect to t = 0
    and solving for t.

    In pre-calculus, you can transform the expression by completing the squares.
    Ax² + Bx + C
    =A(x²+ (B/A)x + C/A)
    =A((x + (B/2A))² + C/A -(B/2A)²)
    From which the maximum is located at
    x+(B/2A) = 0, or
    x= -B/(2A)

    You can substitute the given function to find the maximum.

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