SOLUTION: I am not sure how to start this to figure out the last day of tickets. Use the quadratic equation to determine the last day that tickets will be sold. Write your answer in terms o

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Question 482033: I am not sure how to start this to figure out the last day of tickets.
Use the quadratic equation to determine the last day that tickets will be sold. Write your answer in terms of the number of days after ticket sales begin. (x=1 is the day tickets go on sale).

Tickets=-0.4x^2+9x+11
Answer by jorel1380(2518) About Me  (Show Source):
You can put this solution on YOUR website!
-0.4x^2+9x+11=0
.4x2-9x-11=0
4x2-90x-110=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B-90x%2B-110+=+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=%28-90%29%5E2-4%2A4%2A-110=9860.

Discriminant d=9860 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--90%2B-sqrt%28+9860+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-90%29%2Bsqrt%28+9860+%29%29%2F2%5C4+=+23.6621915873064
x%5B2%5D+=+%28-%28-90%29-sqrt%28+9860+%29%29%2F2%5C4+=+-1.16219158730641

Quadratic expression 4x%5E2%2B-90x%2B-110 can be factored:
4x%5E2%2B-90x%2B-110+=+4%28x-23.6621915873064%29%2A%28x--1.16219158730641%29
Again, the answer is: 23.6621915873064, -1.16219158730641. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-90%2Ax%2B-110+%29

x=23.6621915873064 or -1.16219158730641
Throwing out the negative answer, we get ticket sales to be 0 after the 24th day.