the number of tickets for an upcoming concert is given by N(x)=-0.5x^2+14x+10 where x is the number of days since the concert was announced. When will the tickets peak and how many tickets will be sold that day?

To find the day when the ticket sales will peak and the number of tickets sold on that day, we need to determine the maximum value of the N(x) function.

The given equation is N(x) = -0.5x^2 + 14x + 10

To find the maximum value, we'll use the concept of vertex for a quadratic function. The x-value of the vertex of a quadratic function in the form of f(x) = ax^2 + bx + c can be found using the formula x = -b / (2a).

In our case, the quadratic function is N(x) = -0.5x^2 + 14x + 10, which means a = -0.5, b = 14, and c = 10.

Using the formula, we can calculate the x-value of the vertex:
x = -b / (2a)
x = -14 / (2 * -0.5)
x = -14 / -1
x = 14

So, the x-value of the vertex is 14, which represents the number of days since the concert was announced.

Now, to find the number of tickets sold on that day, we substitute the value of x = 14 into the N(x) equation:
N(14) = -0.5(14)^2 + 14(14) + 10

Simplifying this expression:
N(14) = -0.5(196) + 196 + 10
N(14) = -98 + 196 + 10
N(14) = 108 + 10
N(14) = 118

Therefore, the number of tickets sold on the day when ticket sales will peak is 118.