The number of tickets sold each day for an upcoming performance of Handels Messiah is given by N(x)=-0.4x^2+11.2x+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?
the max will occur at x = 11.2/.8 = 14
To find when the daily ticket sales will peak and the number of tickets sold that day, we need to determine the maximum point of the given function N(x)=-0.4x^2+11.2x+13.
The maximum point of a quadratic function can be found using the vertex formula. Given a quadratic function in the form of f(x) = ax^2 + bx + c, the x-coordinate of the vertex is given by x = -b / (2a).
In our case, the quadratic function is N(x) = -0.4x^2 + 11.2x + 13. Comparing it to the standard form ax^2 + bx + c, we can see that a = -0.4, b = 11.2, and c = 13.
Using the vertex formula, we can calculate the x-coordinate of the vertex:
x = -b / (2a)
x = -11.2 / (2 * (-0.4))
x = -11.2 / (-0.8)
x = 14
Therefore, the x-coordinate of the vertex is 14, which represents the number of days since the concert was first announced when the daily ticket sales will peak.
To find the number of tickets sold on that day, we substitute this x value back into the equation N(x) = -0.4x^2 + 11.2x + 13:
N(14) = -0.4(14)^2 + 11.2(14) + 13
N(14) = -0.4(196) + 156.8 + 13
N(14) = -78.4 + 156.8 + 13
N(14) = 91.4
Therefore, the daily ticket sales will peak on the 14th day since the concert was first announced, and 91.4 (or approximately 91) tickets will be sold that day.