SOLUTION: The number of tickets sold each day for an upcoming performance of Handel's Messiah is given by N(x) = -0.3x^2 + 7.8x + 14, where x is the number of days since the concert was firs

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: The number of tickets sold each day for an upcoming performance of Handel's Messiah is given by N(x) = -0.3x^2 + 7.8x + 14, where x is the number of days since the concert was firs      Log On


   

Question 450003: The number of tickets sold each day for an upcoming performance of Handel's Messiah is given by N(x) = -0.3x^2 + 7.8x + 14, 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?

Found 2 solutions by nerdybill, rwm:
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
N(x) = -0.3x^2 + 7.8x + 14
Looking at the above, we know that it is a parabola that opens downwards (the coefficient associated with the x^2 is negative -- sad face).
Therefore, the vertex is the peak.
x = -b/(2a)
x = -7.8/(2(-0.3))
x = -7.8/(-0.6)
x = 13
.
Number of tickets sold that day (plug it back into original equation):
N(x) = -0.3x^2 + 7.8x + 14
N(13) = -0.3(13)^2 + 7.8(13) + 14
N(13) = 64.7 or 65 tickets

Answer by rwm(914) About Me  (Show Source):
You can put this solution on YOUR website!
-b/2a
-7.8/2*(-.3)
13
plug in 13 for x
On day 13,
64.7 tickets are sold.