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?
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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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