Where to begin?

[Kathy Supper]

The problem states:

You need to supply information about projected ticket dles to the box office manager. The box office manager uses this information to anticipate staffing needs until the tickets sell out. You provide the manager with a quadratic equation that models the expected number of ticket sales for each day x. (x=1 is the day tickets go on sale.)

Tickets= -0.2x^2 + 12x + 11

okay the question asks;

Use the quadratic equation to determine the last day that tickets will be sold.(Note: write your answer in terms of the number of days after ticket sales begin)

My problem is I don't know were to begin with this...I am sure it is easy but not for me at the moment. Can someone direct me in the right direction?

 

[galactus]

The last day tickets will be sold is when they run out.

Set the quadratic to 0 and solve for x, the number of days to sell tickets until they run out.

\(\displaystyle -0.2x^{2}+12x+11=0\)

Try the quadratic formula. You will get two solutions, but only one makes sense.

 

[mmm4444bot]

… determine the last day that tickets will be sold …

The last day tickets will be sold is when they run out …

Hi Kathy:

I do not agree that the last day of sales corresponds to the ticket supply, in this "real-world" senario, as you've posted it.

We're given the following quadratic equation (model).

Tickets = -0.2x^2 + 12x + 11

Clearly, the word 'Tickets' is a variable, but what does this variable represent?

We're told that it represents some expected number of sales. Therefore, this function does not model the ticket supply. In fact, we have no information whatsoever regarding either the total number of tickets available on any given day or even whether or not the show will sell out.

Furthermore, this function generates relatively few whole numbers, when its domain is restricted to whole numbers. Since the variable Tickets represents some number of (expected) sales, then its value must be a whole number. (Technically, this exercise should make a statement about rounding, when defining the meaning of the given quadratic model. However, the absense of such a statement does not change the answer; it's just sloppy.)

I would say that the last day of sales occurs on the day BEFORE the expected number of sales coming out of this model turns negative.

In other words, think about the shape of this model's graph. Since the leading coefficient is negative, we know that the graph is a parabola that opens downward. So, this model tells us that sales figures will be relatively small at first, with increasing sales figures each day until sometime toward the middle of the sales run (when sales are at a maximum), followed by decreasing sales figures each day until some day when the model begins projecting nothing but negative "sales" from that point onward.

So, I view the final day of ticket sales as the last day (chronologically) that the model projects a positive number of expected sales, not if or when the show sells out.

Finally, I'm thinking that the instruction to write the answer in terms of the number of days after day 1 simply means to use an ordinal number, such as in the following examples.

"The 23rd day of sales is the expected last day of sales."

"The 44th day of sales is the expected last day of sales."

"The 71st day of sales is the expected last day of sales."

Basically, start by finding the positive x-intercept (i.e., solve the equation that Galactus posted). If that value is not a whole number, then round it DOWN to the nearest day. If that value is a whole number, then reduce it by 1.

If you would like more help with this exercise, please show us whatever work you can or explain what you're thinking, so that we might determine where to continue helping you.

Cheers,

~ Mark