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?

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) (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 (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=152.8 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: -0.903074280724887, 60.9030742807249. Here's your graph:

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