Help with graphing, vertex and equations.....

[giddensgirl75]

I am so lost of where to start and how to continue. This is my math homework and online math is sooo hard.

1. Suppose you are an event coordinator for a large performance theater. One of the hottest new Broadway musicals has started to tour and your city is the first stop on the tour. You need to supply information about projected ticket sales 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. ( is the day tickets go on sale).

Tickets=-0.3x^2+12x+14

a. Does the graph of this equation open up or down? How did you determine this? Show all your work.


b. Describe what happens to the tickets sales as time passes. Show all your work.



c. Use the quadratic formula to determine the last day that tickets will be sold. Show all your work.

Note. Write your answer in terms of the number of days after ticket sales begin.

d. Will tickets peak or be at a low during the middle of the sale? How do you know?

e. After how many days will the peak or low occur? Show all your work.

f. How many tickets will be sold on the day when the peak or low occurs? Show all your work.

g. What is the point of the vertex? How does this number relate to your answers in parts e. and f?

h. How many solutions are there to the equation ? How do you know? Show all your work.

i. What do the solutions represent? Is there a solution that does not make sense? If so, in what ways does the solution not make sense? Show all your work.

 

[mmm4444bot]

I am so lost

WHY IS THAT ?

online math is sooo hard.

OH. Online class. That's why.

< rant mode on >

It is VERY hard for non-math types to learn math from a machine because YOU become the teacher and student both.

I've seen a few dozen online assignments both from and at various "schools". Many seem to be haphazardly thrown together, without proofreading, containing mis-statements, contradictions, and numerous errors of both the typographical and logical kinds.

The writing is replete with ambiguities.

There are often technical difficulties, on top of everything else.

These experiences leave me with the impression that too many academic administrators are basically fishing for credit-card accounts.

I mean, what's next ? Changing the online-course paradigm (if not for all cirricula) to a video game ?

< rant mode off >


( is the day tickets go on sale) Seems like you did not type the entire statement, here.

Please proofread your post, and fix the error(s) you discover.

These questions are not hard to understand. I will return in about one hour (after eating) and respond to your corrected post line-by-line with example and explanation.

Additionally, let me know whether or not you have graphing capabilities (eg: graphing calculator, software, online grapher).

You need to graph the given equation.

Cheers ~ Mark

 

[giddensgirl75]

Mark,
You are so correct. I should of never taken math online. It is so hard and I am so very lost. if you can help me that would be so awesome. I am sorry I left that part out.

It was suppose to state like this: x=1 is the day tickets go on sale.

This does not make sense still to me. So with any luck it does to you. And yes I have a website I can graph an equation and also equation editor in word. So we might be able to get this.

Thank you again!!
Betty

 

[mmm4444bot]

Hi Betty:

Tickets = -0.3x^2 + 12x + 14

a. Does the graph of this equation open up or down? How did you determine this? Show all your work.

Here's the rule to memorize for determining if the parabola opens upward or downward:

If the leading coefficient is negative, the parabola opens downward; if the leading coefficient is positive, the parabola opens upward.

When a quadratic polynomial is put into the form Ax^2 + Bx + C, the number A is called the "leading coefficient". In other words, you need to inspect the sign of the number that multiplies the squared variable.


b. Describe what happens to the tickets sales as time passes. Show all your work.

Graph y = -0.3x^2 + 12x + 14.

(The symbol y represents the numbers of tickets sold on day x.)

When they ask, "what happens to the ticket sales as time passes", they mean "what happens to the values of y as x starts at 1 and grows". In other words, does y continually get bigger, smaller, does it decrease then rise or rise then decrease. Look at the curve, to answer this question.


c. Use the quadratic formula to determine the last day that tickets will be sold. Show all your work.

Do you know the Quadratic Formula ?

The number of tickets sold on day x (that is, y) cannot become negative because it does not make sense to sell a negative number of tickets.

To determine the "last" positive, Whole-numbered value of x that makes sense in this mathematical model, let y = 0 and use the Quadratic Formula to find the solutions for x. If you look at your graph, you can estimate the rightmost x-intercept. Perhaps, if your graph is good enough, you'll also see that this x-intercept is not a Whole number.

Therefore, after you get that solution from the Quadratic Formula, you need to round it to the nearest Whole number, such that y is still positive there.

If this is too much to understand at once, try to solve the following equation and show us your work:

-0.3x^2 + 12x + 14 = 0



Note. Write your answer in terms of the number of days after ticket sales begin.

Oh, this is a little tricky. I almost read it to mean "after" day 1. But, I'm thinking that the instructor meant to write "since ticket sales began", so use the rounded result as described above.


d. Will tickets peak or be at a low during the middle of the sale? How do you know?

This is the same as asking if the parabola has a high point or low point. It's obvious, when looking at the graph. Or, just realize that parabolas that open upward have a "low" point (vertex is a minimum), and parabolas that open downward have a "high" point (vertex is a maximum).



e. After how many days will the peak or low occur? Show all your work.

Any "peak" or "low" occurs at the vertex. There is a formula to memorize that provides the x-coordinate of the vertex point. It's the part of the Quadratic Formula that's left over, if you remove the radical term.

x-coordinate of vertex = -B/(2A)

So, substitute in the values of B and A and simplify; then you'll know where the vertex occurs. I mean, the result is x at the "peak", so that's the number of days it takes for sales to peak.



f. How many tickets will be sold on the day when the peak or low occurs? Show all your work.

Substitute your result for the x-coordinate at the vertex point into the equation, and do the arithmetic, to find y (the number of tickets sold on that day).

y = -0.3x^2 + 12x + 14


g. What is the point of the vertex? How does this number relate to your answers in parts e. and f?

Hmmm, parts (e) and (f) already yielded the coordinates of the vertex point, so this question seems redundant, to me.

Just report the coordinates of the vertex point, and say that they're identical to the results in parts (e) and (f).


h. How many solutions are there to the equation ? How do you know? Show all your work.

This question is poorly worded. I'm thinking they means the equation WHEN y = 0.

You should already know because you used the Quadratic Formula above to find them. Alternatively, you could look at the graph and realize that each x-intercept corresponds to a solution of the equation. (Of course, the negative solution makes no sense, in terms of the meaning of x. So this equation only models tickets sales for a restricted domain of positive x-values.)


i. What do the solutions represent? Is there a solution that does not make sense? If so, in what ways does the solution not make sense? Show all your work.

What do you think ?

Please show any work that you can, and try to ask specific questions, if you get confused.

Read my post carefully; I pretty much spit it out off the top of my head without much proofreading because I'm pressed for time, right now. (I'll check back here in a few hours.)

Cheers ~ Mark

 

[mmm4444bot]

Betty, did you have an opportunity to work on this exercise again ?

If my post above is too confusing, let me know. I was rushed, so I did not have time to include examples or diagrams. (Maybe I used too much math terminology.)

I can include diagrams and examples, if you need specific help. Please give me some idea about what parts are confusing.

If you are done with this exercise, you do not need to respond.

Cheers ~ Mark