SOLUTION: Please help. The number of tickets sold each day for a performance is given by N(x)=-0.5x^2+10x+13, where x is the number of days since the concert was first announced. When wil

Algebra ->  Equations -> SOLUTION: Please help. The number of tickets sold each day for a performance is given by N(x)=-0.5x^2+10x+13, where x is the number of days since the concert was first announced. When wil      Log On


   

Question 132300: Please help.
The number of tickets sold each day for a performance is given by N(x)=-0.5x^2+10x+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?
Thank you.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Remember, the peak occurs at the vertex.

To find the vertex, we first need to find the axis of symmetry (ie the x-coordinate of the vertex)
To find the axis of symmetry, use this formula:

x=-b%2F%282a%29

From the equation y=-0.5x%5E2%2B10x%2B13 we can see that a=-0.5 and b=10

x=%28-10%29%2F%282%2A-0.5%29 Plug in b=10 and a=-0.5


x=%28-10%29%2F%28-1%29 Multiply 2 and -0.5 to get -1


x=10 Divide


So the axis of symmetry is x=10


So the x-coordinate of the vertex is x=10. Lets plug this into the equation to find the y-coordinate of the vertex.


Lets evaluate f%2810%29



f%28x%29=-0.5x%5E2%2B10x%2B13 Start with the given function


f%2810%29=-0.5%2810%29%5E2%2B10%2810%29%2B13 Plug in x=10


f%2810%29=-0.5%2A100%2B10%2A10%2B13 Raise 10 to the 2nd power to get 100


f%2810%29=-50%2B10%2A10%2B13 Multiply -.5 and 100 to get -50


f%2810%29=-50-100%2B13 Multiply 10 and 10 to get 100


f%2810%29=50%2B13 Add -50 and 100 to get 50


f%2810%29=63 Add 50 and 13 to get 63


So when x=10, we have y=63


So the vertex is (10,63)


So on the 10th day, the tickets sales will peak at 63