The point of the vortex is .. what?

[HotelPaper]

The problem original problem was:
Tickets = -0.2x^2+12x+11
It applies to an employee giving their boss an equation to estimate how many tickets will be sold for a huge musical number coming to down in the theater.

The equation below is the max number of days (the x = 60) before the tickets go into the negative and the manager of the theater loses money.
Tickets = -0.2(60)^2+12(60)+11

Now the 60 in the ()'s is the most tickets that can be sold before it begins to go into the negatives. It equals 11 tickets. Beyond that, the manager of the theater is losing money. What my teacher wants now is to find the point of the vortex, and how many solutions there are. I also don't understand what he means by asking me what the solutions represent. Could someone help me solve this?

 

[Deleted member 4993]

The problem original problem was:
Tickets = -0.2x^2+12x+11
It applies to an employee giving their boss an equation to estimate how many tickets will be sold for a huge musical number coming to down in the theater.

The equation below is the max number of days (the x = 60) before the tickets go into the negative and the manager of the theater loses money.
Tickets = -0.2(60)^2+12(60)+11

Now the 60 in the ()'s is the most tickets that can be sold before it begins to go into the negatives. It equals 11 tickets. Beyond that, the manager of the theater is losing money. What my teacher wants now is to find the point of the vortex, and how many solutions there are. I also don't understand what he means by asking me what the solutions represent. Could someone help me solve this?

Before you start to solve the problem:

make sure you know - what 'x' is? Also you write "vortex" - however I think you mean "vertex".

then plot the function.

What is the name of the curve that you see? Is there a maximum or minimum in the curve? Where does it cross x-axis?

What do you learn from the plot? - tell us - then we can guide you properly to the answer.