The number of tickets sold each day for an upcoming performance of Handel’s Messiah is given by N(x)=-0.4x²+9x+11, where x is the expected number of ticket sales per day. x=1, the day tickets go on sale. After how many days will the peak or low occur?
You have y = -0.4x^2 + 9x + 11 = ax^2 + bx + c, so a = -0.4, b = 9, and c = 11.
Plug "a" and "b" into the formula for the vertex
. . . . .
So the peak will be at x = 11.25. Since "x = 1" is the first day, then 11.25 - 1 = 10.25 is the number of days after
the opening day.
How many tickets will be sold that day?
Plug the value of "h" into the quadratic to find the number of tickets for that day.
In addition how do I find the last day tickets will be sold?
Since you can't sell negative numbers of tickets, find the location of the zeroes (by plugging "0" in for "N" and then solving the quadratic equation
, probably by using the Quadratic Formula
). One won't make practical sense (you can't sell tickets before sales open, so x-values less than "1" or "0" can't be right), but the other will tell you when sales have declined to zero, at which you'll want to stop trying to sell tickets.
If you get stuck, please reply showing how far you have gotten. Thank you!