SOLUTION: The number of tickets sold each day for an up coming performance of Handel's Messiah is given by N(x)=-0.4x^2+8.8x+12, where x is the number of days since the concert was 1st annou

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: The number of tickets sold each day for an up coming performance of Handel's Messiah is given by N(x)=-0.4x^2+8.8x+12, where x is the number of days since the concert was 1st annou      Log On


   

Question 335717: The number of tickets sold each day for an up coming performance of Handel's Messiah is given by N(x)=-0.4x^2+8.8x+12, where x is the number of days since the concert was 1st announced. When will the daily tickets sales peak and how many tickets will be sold that day?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
N%28x%29=-0.4x%5E2%2B8.8x%2B12
Because of the x%5E2 term this is a parabola. And since the coefficient of the x%5E2 term is negative the parabola opens downward. For a downward opening parabola, the maximum value will be at the vertex.

The x coordinate of the vertex for any vertically oriented parabola is %28-b%29%2F2a. So the x coordinate of this parabola is:
x+=+%28-b%29%2F2a+=+%28-8.8%29%2F2%28-0.4%29+=+%28-8.8%29%2F%28-0.8%29+=+11

So the maximum number of tickets will be sold 11 days after the announcement of the concert. The number of tickets sold on that day is:
N%2811%29+=+-0.4%2811%29%5E2+%2B+8.8%2811%29+%2B+12
N%2811%29+=+-0.4%28121%29+%2B+8.8%2811%29+%2B+12
N%2811%29+=+-48.4+%2B+96.8+%2B+12
N%2811%29+=+60.4
So there will be approximately 60 tickets sold that day.