The number of tickets sold each day for an upcoming performance of Handel's messiah is given by N (x) = 0.4x^2 + 11.2x + 12 where x is the number of days since the concert was first announced. when will daily tickets sales peak and how many tickets will be sold that day?
You must have copied something wrong.
N(x) as you have written it will increase with x. There will be no peak.
Are you sure there isn't supposed to be a minus sign in front of 0.4x^2?
Try making a graph to find the answer, once you have verified the correct equation. I recommend you round off N(x) to the nearest integer.
To find out when the daily ticket sales will peak and how many tickets will be sold on that day, we need to find the vertex of the quadratic function.
The vertex form of a quadratic equation is given by:
f(x) = a(x - h)^2 + k
Where (h, k) represents the coordinates of the vertex.
In the given equation N(x) = 0.4x^2 + 11.2x + 12, we can see that a = 0.4, b = 11.2, and c = 12.
The x-coordinate of the vertex can be found using the formula:
h = -b / (2a)
For our equation, h = -11.2 / (2 * 0.4) = -11.2 / 0.8 = -14.
Substituting this value back into the original equation, we can find the y-coordinate of the vertex:
N(h) = 0.4(-14)^2 + 11.2(-14) + 12
N(h) = 0.4(196) - 156.8 + 12
N(h) = 78.4 - 156.8 + 12
N(h) = -66.4
Therefore, the vertex (h, k) is (-14, -66.4). This means that the peak in the daily ticket sales will occur on the 14th day since the concert was announced, and the number of tickets sold that day will be -66.4 (rounded to the nearest whole number).
Please note that the calculated value is negative, which may not be meaningful in this context. It could indicate that the highest point is actually a minimum rather than a maximum. You may want to double-check the equation or the given information to ensure accuracy.