OK. I think I have my head around most of this but for one question. I have plotted a graph with the quadratic equation tickets=-02x^2+12x+11.

Question

My graph opens down and shows I will sell tickets for 60 days peaking at the vertex at 30 days where I sell 191 tickets.

Now I have to use the quadratic equation to determine the last day that tickets will be sold. (its the 60th day)I need to write my answer in terms of the number of days after ticket sales begin. I wish they could just use terms instead of words. How do I write the equation to answer the question?

Answer 1

I think you left out a decimal point in your equation. It should read
N = -0.2x^2 + 12x + 11
where N is the number sold on day x. That does result in a maximum of 191 on day 30.

If you assume that tickets stop being sold when N=0, then solve
-0.2x^2 + 12x + 11 = 0 for that day.
That's the same at
-x^2 + 60 x +55 = 0
The answer is x = 60.9 days
After 60 days, the number sold becomes negative, so the equation can no longer be valid.

Answer 2

Got it. Thank you