Quadratic Equations and Functions: number of tickets sold

[aainsworth]

Hello. Here is a problem similar to one I am having trouble solving. If I could get help solving this problem, I would be able to solve my actual problem...

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? How many tickets will be sold that day? In addition how do I find the last day tickets will be sold? And how do I find the point of vertex for this function? How does this number relate to the questions "after how many days will the peak or low occur and how many tickets will be sold that day?" Furthermore, how many solutions will the function have? Is there a solution that does not make sense. If so, what ways will it not make sense?

I do not know how to find the peak day and low days or anything like that. I really need some assistance.

Regards,

Angela Ainsworth

[stapel_eliz]

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!

[aainsworth]

Okay. As far as how many tickets will be sold that day. I do not understand where to plug h into. In addition, I do not understand this information: "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."

[stapel_eliz]

Okay. As far as how many tickets will be sold that day. I do not understand where to plug h into.

You are given an equation, N(x) = -0.4x^2 + 9x + 11. You have been given a value for x; namly, x = h.

To learn about function notation and how to "plug the value for h in for x in N(x)", try here.

I do not understand this information: "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).

I will guess that you mean that you aren't familiar with the Quadratic Formula. To learn how to use it, try here.