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
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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) (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:
From the equation we can see that a=-0.5 and b=10
Plug in b=10 and a=-0.5
Multiply 2 and -0.5 to get -1
Divide
So the axis of symmetry is
So the x-coordinate of the vertex is . Lets plug this into the equation to find the y-coordinate of the vertex.
Lets evaluate
Start with the given function
Plug in
Raise 10 to the 2nd power to get 100
Multiply -.5 and 100 to get -50
Multiply 10 and 10 to get 100
Add -50 and 100 to get 50
Add 50 and 13 to get 63
So when , we have
So the vertex is (10,63)
So on the 10th day, the tickets sales will peak at 63
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