SOLUTION: Please help me solve: The number of tickets sold for a Broadway musical is given by N(x)= -0.4x^2 + 12x + 12 where "x" is the number of days since the concert was first announced.

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Question 466765: Please help me solve: The number of tickets sold for a Broadway musical is given by N(x)= -0.4x^2 + 12x + 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?
N(x)= -0.4x^2 + 12x + 12
Answer by ccs2011(207) About Me  (Show Source):
You can put this solution on YOUR website!
Since this is a quadratic function, its graph is parabolic.
The leading coefficient(-0.4) is negative, this tells us its a downward pointing parabola.
The vertex of this parabola will give us the maximum value of N(x) or the highest daily ticket sales and the day it occurred.
To find vertex, first find line of symmetry or x_coordinate of vertex.
x+=+%28-b%29%2F2a
where
a = -0.4
b = 12
c = 12
x+=+%28-12%29%2F2%28-0.4%29
x+=+15
Substitute this value into function
y+=+-0.4%2815%5E2%29+%2B+12%2815%29+%2B+12
y+=+-90+%2B+180+%2B+12
y+=+102
Vertex: (15,102)
Thus, on the 15th day ticket sales peaked at 102 tickets sold.