Emilie Exavier
$11 / 14 / 2312: 06 \mathrm{~A}$
The number of tickets sold each day for an upcoming performance of Handel's Messiah is given by $N(x)=-0.4 x^{2}+9.6 x+13$, 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?

Step 1 ：The problem is asking for the maximum point of the quadratic function \(N(x)=-0.4 x^{2}+9.6 x+13\). This is a parabola that opens downwards because the coefficient of \(x^2\) is negative.

Step 2 ：The maximum point of a parabola \(y=ax^2+bx+c\) is given by \(x=-\frac{b}{2a}\). We can use this formula to find the day when the ticket sales will peak.

Step 3 ：After finding the value of \(x\), we can substitute it back into the function to find the number of tickets sold that day.

Step 4 ：By solving, we find that \(x = 12\), which means the ticket sales will peak on the 12th day after the concert was first announced.

Step 5 ：Substituting \(x = 12\) back into the function, we find that \(N = 70.6\), which means approximately 71 tickets will be sold that day (since we can't sell a fraction of a ticket).

Step 6 ：So, the final answer is \(\boxed{12, 71}\). The daily ticket sales will peak on the 12th day after the concert was first announced, and the number of tickets sold that day will be approximately 71.