SOLUTION: The equation is tickets= -0.2x^2+12x+11. what would be the last day tickets are sold? How many days would the peak occur?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: The equation is tickets= -0.2x^2+12x+11. what would be the last day tickets are sold? How many days would the peak occur?      Log On


   

Question 178883: The equation is tickets= -0.2x^2+12x+11.
what would be the last day tickets are sold? How many days would the peak occur?
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
The equation is tickets= -0.2x^2+12x+11.
.
By inspecting the coefficient associated with the x^2 term, we see that it is negative therefore the parabola is opens downward. If so, finding the vertex will tell us the maximum.
.
axis of symmetry = -b/2a
= -12/(2(-0.2))
= -12/(-0.4)
= 30 days (days would the peak occur)
.
Setting the equation to zero then solve for x:
0 = -0.2x^2+12x+11
Since we can't factor, solve using the quadratic equation. Doing so, yields:
x = {-0.9, 60.9}
Tossing out the negative solution the answer is:
61 days (number of days before tickets are sold)
.
Details of quadratic:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -0.2x%5E2%2B12x%2B11+=+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=%2812%29%5E2-4%2A-0.2%2A11=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-%2812%29%2Bsqrt%28+152.8+%29%29%2F2%5C-0.2+=+-0.903074280724887
x%5B2%5D+=+%28-%2812%29-sqrt%28+152.8+%29%29%2F2%5C-0.2+=+60.9030742807249

Quadratic expression -0.2x%5E2%2B12x%2B11 can be factored:
-0.2x%5E2%2B12x%2B11+=+-0.2%28x--0.903074280724887%29%2A%28x-60.9030742807249%29
Again, the answer is: -0.903074280724887, 60.9030742807249. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-0.2%2Ax%5E2%2B12%2Ax%2B11+%29