SOLUTION: When dealing with the quadratic equation f(x)=-0.2x^2+12x+11, where the function represents the expected number of ticket sales each day, and x=1 is the day tickets go on sale. M

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: When dealing with the quadratic equation f(x)=-0.2x^2+12x+11, where the function represents the expected number of ticket sales each day, and x=1 is the day tickets go on sale. M      Log On


   



Question 596129: When dealing with the quadratic equation f(x)=-0.2x^2+12x+11, where the function represents the expected number of ticket sales each day, and x=1 is the day tickets go on sale.
My main question is, using this equation how can I determine the last day that tickets will be sold?

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
f(x)=-0.2x^2+12x+11
since f(x) represents the number of tickets sold
to find the last day tickets were sold, set f(x) to zero and solve for x:
f(x)=-0.2x^2+12x+11
0=-0.2x^2+12x+11
0=0.2x^2-12x-11
applying the quadratic formula, we get:
x = {60.9, -0.9}
we can toss out the negative solution (extraneous) leaving:
x = 60 days
.
details of quadratic follows:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 0.2x%5E2%2B-12x%2B-11+=+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=%28-12%29%5E2-4%2A0.2%2A-11=152.8.

Discriminant d=152.8 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--12%2B-sqrt%28+152.8+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-12%29%2Bsqrt%28+152.8+%29%29%2F2%5C0.2+=+60.9030742807249
x%5B2%5D+=+%28-%28-12%29-sqrt%28+152.8+%29%29%2F2%5C0.2+=+-0.903074280724887

Quadratic expression 0.2x%5E2%2B-12x%2B-11 can be factored:
0.2x%5E2%2B-12x%2B-11+=+0.2%28x-60.9030742807249%29%2A%28x--0.903074280724887%29
Again, the answer is: 60.9030742807249, -0.903074280724887. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+0.2%2Ax%5E2%2B-12%2Ax%2B-11+%29