SOLUTION: I need help with this problem: The number of tickets sold each day for an upcoming performance of Handels Messiah is given by N(x)=-0.3^2+7.8x+12, where x is the number of days si

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I need help with this problem: The number of tickets sold each day for an upcoming performance of Handels Messiah is given by N(x)=-0.3^2+7.8x+12, where x is the number of days si      Log On


   

Question 155721: I need help with this problem:
The number of tickets sold each day for an upcoming performance of Handels Messiah is given by N(x)=-0.3^2+7.8x+12, 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? (I don't know how to go about doing this problem)
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
N(x)= -0.3^2+7.8x+12, 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?
:
Notice that this is a quadratic equation, if we find the axis of symmetry we can
find the maximum (vertex);
:
Find the axis of symmetry using the formula x = -b/(2a)
In this equation it would be
x = %28-7.8%29%2F%282%2A-.3%29
x = %28-7.8%29%2F%28-.6%29
x = +13 days from the announcement for max ticket sales
:
Find the max number of tickets by substituting 13 for x in the equation:
N(x)= -0.3^13^2 + 7.8(13) + 12
N(x) = -.3(169) + 101.4 + 12
N(x) = -50.7 + 101.4 + 12
N(x) = 62.7 ~ 63 is the maximum tickets sold.
:
Did this make sense to you now?