Question 290506: The number of tickets sold each day for an upcoming performance of Handels Messieah is given by N(x)=-0.5^2+11x+13, 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 __
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! The number of tickets sold each day for an upcoming performance of Handels Messieah is given by N(x)=-0.5^2+11x+13, 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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The given equation:
N(x)=-0.5x^2+11x+13
is a parabola that opens downward -- because the coefficient associated with the x^2 term is negative. So, if you find the "vertex" it will give you the maximum.
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Finding the "axis of symmetry" will give you the "number of days" after announcement that the ticket sales reached its peak:
x = -b/(2a)
x = -11/(2(-0.5))
x = -11/(-1)
x = 11 days
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To find the number of tickets sold, plug in the value above back into:
N(x)=-0.5x^2+11x+13
N(11)=-0.5(11^2)+11(11)+13
N(11)=-0.5(121)+(121)+13
N(11)=-60.5+134
N(11)=73.5
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Ticket sales will peak 11 days after the concert was first announced. The number of tickets sold on that day will be 73.
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