Question

the number of tickets sold each day for an upcoming performance of handel’s messiah is given by ( n = -0.3x^2 + 9x + 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 (square) days after the concert was first announced

Explanation:

Step1: Identify quadratic form

The function is $N(x) = -0.3x^2 + 9x + 13$, a downward-opening quadratic ($a=-0.3<0$), so its vertex is the maximum point.

Step2: Calculate peak day (x-coordinate of vertex)

For $ax^2+bx+c$, vertex x is $-\frac{b}{2a}$.
$x = -\frac{9}{2\times(-0.3)} = \frac{9}{0.6} = 15$

Step3: Calculate peak ticket sales

Substitute $x=15$ into $N(x)$.
$N(15) = -0.3(15)^2 + 9(15) + 13 = -0.3(225) + 135 + 13 = -67.5 + 135 + 13 = 80.5$

Answer:

Ticket sales will peak 15 days after the concert was first announced, and 80.5 tickets will be sold that day.