The number of tickets soldeach day for an upcoming performance of Handiel Messiah is given by N(x)=-0.4x^2+9.6x+10,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.
Treat the equation as a parabola, find its vertex. When? what is the axis of symettry?
To find the day when daily ticket sales peak and the number of tickets sold on that day, we need to find the vertex of the quadratic function N(x) = -0.4x^2 + 9.6x + 10.
The vertex of a quadratic function in the form f(x) = ax^2 + bx + c is given by the formula x = -b / (2a). In our case, a = -0.4 and b = 9.6.
Using the formula, we can find x = -9.6 / (2 * -0.4) = 12.
So, the peak of ticket sales will happen on the 12th day since the concert was announced.
To determine the number of tickets sold on that day, we substitute x = 12 into the equation N(x) = -0.4x^2 + 9.6x + 10:
N(12) = -0.4 * 12^2 + 9.6 * 12 + 10
N(12) = -0.4 * 144 + 115.2 + 10
N(12) = -57.6 + 125.2
N(12) = 67.6
Therefore, the peak sales will occur on the 12th day, and 67 tickets will be sold on that day.