SOLUTION: tHE NUMBER OF TICKETS SOLD EACH DAY FOR AN UPCOMING PERFORMANCE OF HANDELS MESSIAH IS GIVEN BY N(x)=-0.5x^2+11x+15, where x is the number of days since the concert was first anno

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Question 408782: tHE NUMBER OF TICKETS SOLD EACH DAY FOR AN UPCOMING PERFORMANCE OF HANDELS MESSIAH IS GIVEN BY N(x)=-0.5x^2+11x+15, 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?
Tickets sales will peak _______ days af ter thec onvert was first announced.
The number of tickets sold on that day will be ______
(round to the nearest integer)
Answer by graphmatics(170) About Me  (Show Source):
You can put this solution on YOUR website!
+graph%28+300%2C+200%2C+-10%2C+50%2C+-10%2C+90%2C+-0.5x%5E2%2B11x%2B15%29+
Now if we could just find the 2 x values where the graph
crosses the X axis. We can use the quadratic equation and get

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -0.5x%5E2%2B11x%2B15+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2811%29%5E2-4%2A-0.5%2A15=151.

Discriminant d=151 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-11%2B-sqrt%28+151+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2811%29%2Bsqrt%28+151+%29%29%2F2%5C-0.5+=+-1.28820572744451
x%5B2%5D+=+%28-%2811%29-sqrt%28+151+%29%29%2F2%5C-0.5+=+23.2882057274445

Quadratic expression -0.5x%5E2%2B11x%2B15 can be factored:
-0.5x%5E2%2B11x%2B15+=+-0.5%28x--1.28820572744451%29%2A%28x-23.2882057274445%29
Again, the answer is: -1.28820572744451, 23.2882057274445. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-0.5%2Ax%5E2%2B11%2Ax%2B15+%29


so we get x=-1.2 and x=23.28. Now lets see 23.28 - (23.28+1.2)/2 = 11.
So it's 11 days of ticket sale increase from the -1.2 intercept. We probabily
want to start a day = 0 so take 1 day off and get 10 days to peak.