## Quadratic Equations and Functions: number of tickets sold

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.

### Quadratic Equations and Functions: number of tickets sold

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
aainsworth

Posts: 4
Joined: Sun Apr 05, 2009 1:16 am

aainsworth wrote: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:

. . . . .$h\, =\, \frac{-b}{2a}\, =\, \frac{-9}{-0.8}\, =\, 11.25$

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.

aainsworth wrote: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.

aainsworth wrote: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!

stapel_eliz

Posts: 1756
Joined: Mon Dec 08, 2008 4:22 pm

### Re: Quadratic Equations and Functions: number of tickets sold

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."
aainsworth

Posts: 4
Joined: Sun Apr 05, 2009 1:16 am

### Re: Quadratic Equations and Functions: number of tickets sold

aainsworth wrote: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.

aainsworth wrote: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.

stapel_eliz

Posts: 1756
Joined: Mon Dec 08, 2008 4:22 pm