Question

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).


a. Does the graph of this equation open up or down? How did you determine t

Answer 1

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

b. Describe what happens to the tickets sales as time passes.

c. 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.

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?

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

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?

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?

Answer 2

i think its graph shoul be +ve

Answer 3

think we are missing a piece of information yes?

Answer 4

usually something like "for every dollar increase in price there are 3 less tickets sold" or something

Answer 5

the numbers of tickets increase and then hit a plateu then begin to drop; opens down

Answer 6

without the equation to go by; you cant really determine the rest of it

Answer 7

because i am almost certain that you will have something like
\[y=ax^2+bc+c\] with a negative number for a. then
1) the equation opens down
2) as time passes first then increase and then decrease
3) guess we need the equation for this one
4) ditto. need the vertex
am i missing something??

Answer 8

haven't given this award for a while

Answer 9

Ticket= -0.2x^2+12x+11 is the equation that I didnt not get in there sorry

Answer 10

aaaaaaaaaaaaaaaaaaaaaaaah

Answer 11

now we have it all!

Answer 12

\[T(x)=-0.2x^2+12x+11\]

Answer 13

a) parabola faces down
b) ticket sales first increase and then decrease as time goes on

Answer 14

c) set = 0 and solve to get
\[0= -0.2x^2+12x+11\]
or
\[-2x^2+120x+110=0\] or better yet
\[x^2-60x-55=0\] and use the quadratic formula to solve for x.

Answer 15

We look at the general quadratic
\[q(x) = ax^{2} + bx + c,\]where a is nonzero. If
a > 0, then the parabola is comcave upward, hence it has a global minimum at
(-b/(2a), q(-b/(2a)).

Answer 16

you should get something close to 61

Answer 17

i came across this version of the quad formula
\[\frac{-2c}{b\pm\sqrt{b^2-4ac}}\]

Answer 18

If a < 0, the parabola is concave downward, then we have a global maximun at
(-b/(2a), q(-b/(2a)).

Answer 19

you will have peak sales at vertex of this parabola, which will occur at
\[-\frac{b}{2a}\] where
\[a=-.2,b=12\] so
\[-\frac{b}{2a}=-\frac{12}{2\times -.2}=\frac{12}{.4}=\frac{120}{4}=30\]

Answer 20

peak sales in 30 days. the number of sales will be whatever you get when you replace x by 30 in original expression

Answer 21

the point of the vertex is
\[(30,T(30))\] which represents the day of the peak sales (day 30) and the number of sales you get on that day (i will let you compute this)

Answer 22

by the last question i assume it means how many solutions to the equation
\[.2x^2+12x+11=0\] are there, and there are 2, but the negative one does not make sense in this context because you cannot go back in time. wish sometimes, but it is impossible

Answer 23

and that is that

Answer 24

so what is c,d,e,f,g,h then I am confused

Answer 25

ss can u help more please

Answer 26

How do u determine that the parabola faces down?

Answer 27

If the highest term has a negative coefficient

Answer 28

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

Answer 29

Look at the leading coefficient. _t's -0.2, a negative number, so the parabola is concave downward, so it has a peak, or global maximun.

Answer 30

so that is the answer to d.?

Answer 31

It will peak during the middle of the sale.

Answer 32

how do we know?

Answer 33

To get the peak value, a = -.2, b = 12, c = 11,-
-b/(2a) = -(12/(-.4) = 30. The thirtieth day is when you have peak ticket sales. To determine how many tickets sold on that day, evaluate
\[-0.2 x^{2}+ 12 x + 11\]at x = 30.

Answer 34

On the thirtieth day of ticket sales, 3,431 tickets are sold.

Answer 35

I am trying to finish d what was that?

Answer 36

hero can you help me please?

Answer 37

abtrehearn is right

Answer 38

It will peak

Answer 39

The answer to d is that ticket sales will peak during the middle of the sale. The reason is that the graph is concave downward (leading coefficient is negative), so it has a peak at the middle of the sale.

Answer 40

ok I need to rest of them to please?

Answer 41

abtrehearn also revealed that the peak will occur on the 13th day and the ticket sales will be 3,431.

Answer 42

To work part e, get the vertex pf the parabola. Its x-coordinate is -b/(2a) = -12/(-.4) = -30. Peak ticket sales occur on the thirtieth day of the sale. That answers part e.

Answer 43

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

Answer 44

-12/(-.4 = 30, not -30.

Answer 45

Peak sales occur on day 30 of the sale.

Answer 46

how do we know?

Answer 47

Do you renenber how to find the vertex of a parabola?

Answer 48

How does this number relate to your answers in parts e. and f?

Answer 49

It gives you when maximum ticket sales occur and how many tickets are sold that day.

Answer 50

The x-coordinate is when maximum sales occur, and the y-coordinate of the vertex gives you how many tickets are sold that day.

Answer 51

Takd a look at the graph of
\[y = -0.2 x^{2} + 12x + 11.\]

Answer 52

How many solutions are there to the equation ? How do you know?

Answer 53

ok

Answer 54

Do you see where the peak is?

Answer 55

There's most likely two solutions

Answer 56

According to the graph that I seen there is no peak

Answer 57

Did you make sure that there was a negative afront the highest coefficient?

Answer 58

yes

Answer 59

I'm going to post what it should look like

Answer 60

http://www.wolframalpha.com/input/?i=y+%3D+-0.2+x^2+%2B+12x+%2B+11.

Answer 61

According to the function you posted....it has one peak and two solutions

Answer 62

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?

Answer 63

ok that helped some

Answer 64

Any solution that is negative will not make sense

Answer 65

what ways does it now make sense please

Answer 66

there's no such thing as negative days

Answer 67

First we need to find the solutions

Answer 68

The solutions I have are (-0.903,0) and (60.9, 0)

Answer 69

Basically the one that's negative obviously doesn't make sense

Answer 70

The other one means that after 60 days, the sale is over.