SOLUTION: The number of tickets sold each day for an upcoming performance of Handel's Messiah is given by N(x)=-0.5x^2+14x+11, where x is the number of days since the concert was first annou

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Question 626562: The number of tickets sold each day for an upcoming performance of Handel's Messiah is given by N(x)=-0.5x^2+14x+11, where x is the number of days since the concert was first announced. When will daily ticket sales peak and how many tickets will be sold that day?
Ticket sales will peak ____ days after the concert was first announced.

The number of tickets sold on that day will be _____.
Is the peak where the minimum/maximum of the vertex is? I am confused on how to find both answers.
Any help is greatly appreciated. Thank you.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The number of tickets sold each day for an upcoming performance of Handel's Messiah is given by N(x)=-0.5x^2+14x+11, where x is the number of days since the concert was first announced. When will daily ticket sales peak and how many tickets will be sold that day?
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Peak occurs when x = -b/(2a) = -14/(2*-0.5) = 14

Ticket sales will peak 14 days after the concert was first announced.
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The number of tickets sold on that day will be 305
# sold = f(14) = -(1/2)14^2+14*14+11 = (3/2)14^2+11 = 305
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Is the peak where the minimum/maximum of the vertex is?
Peak is a maximum.
Note: Your quadratic has a maximum value because the
coefficient of x^2 is negative.
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Cheers,
Stan H.
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