MAT 117 appendix F. solution enclosed here in the file..

mat117_appendix_f.eqedit.sol_. x

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. (x=1 is the day tickets go on sale).  Tickets -2x^2+22x+13

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

2.     
Describe what happens to the tickets sales as time passes.

     3.  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.

    

       

               

4Will tickets peak or be at a low during the middle of the sale? How do you know?

       

5. After how many days will the peak or low occur?

 

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

  

7.What is the point of the vertex? How does this number relate to your answers in parts 5 and 6 ?

    8.  How many solutions are there to the equation? 
-2x^2+22x+13= 0 How do you know?

There are two solutions to the problem since it is of degree 2 and quadratic equation.

    9.  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? .

    

Suppose

you are an event coordinat

or

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 bo

x

office manager. The box office

manager uses this information to anticipate staffing needs until the tickets sell out. You

provide the manager with a quadrati

c equation that models the expected number of ticket

sales for each day x. (x

=

1 is the day tickets go on sale).

 

Tickets

–

2

x^2

+

22

x+

13

1.

Does the graph of this equation open up or down

?

How did you determine this?

The graph of this equation

DOWN

,

because lead coefficient is a NEGATIVE

2.

Describe what happens to the tickets sales as time passes.

Because of the bent down form of the parabolic

graph

ticket sales

will increase

,

then reaches maximum

and

then decreases

     

3.

 

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.

.

.

.

x=

–

0.

5

6

or 11.56

Take only positive solution since number of days can never be

negative

x=

11.5

6

or

say

12

.

On the

12th

day, the ticket sales go to zero.

4

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

Peak; the parabola has a maximum at middle point.

5.

After how many days will the peak or low occur?

The peak value occurs at x=

.

6.

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

Substitute x=

6

in equation for y.

.
.
−

72+132+13.

.

7.What is the point of the vertex? How does this number relate to your answers in parts 5 and 6 ?

Vertex is (.

.
.

x-coordinate of the vertex gives the days when peak value of the tickets sold.

y -coordinate of the vertex gives maximum number of tickets sold.

    8.  How many solutions are there to the equation?   = 0 How do you know?

There are two solutions to the problem since it is of degree 2 and quadratic equation.

A quadratic equation has two solutions.

If Discriminate D=

Here D=

Hence two solutions.

    9.  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? .

 

When solving we will get one positive solution and one negative solution,.

The negative solution does not make sense because number of days never be negative.

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 quadrati
c equation that models the expected number of ticket
sales for each day x. (x=1 is the day tickets go on sale).

Tickets
–
2x^2+22x+13

1.

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

The graph of this equation
DOWN, because lead coefficient is a NEGATIVE

2.

Describe what happens to the tickets sales as time passes.

Because of the bent down form of the parabolic

graph
ticket sales

will increase
,
then reaches maximum
and
then decreases

3.

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.

??

=
–
??

±

?
??
2
–
4

????

2
??
.

–
22
±
?
2
2
2
–
4

*

–
2
*
13
2
*
–
2
.

–
22
±
?

484

+

104

–
4

–
2
2
±
?

588

–
4

–
2
2
±

24

.

25

–
4

??
=
–
22
+
24
.
25
–
4
,
–
2
2
–
24
.
25
–
4
.

x=
–
0.56 or 11.56

Take only positive solution since number of days can never be
negative

x
=
11.56

or

say
12
.

On the
12th

day, the ticket sales go to zero.

4
Will tickets peak or be at a low during the middle of the sale? How do you know?

Peak; the parabola has a maximum at middle point.

5
.
After how many days will the peak or low occur?

The peak value occurs at x=
–
??
2
??
.

??
=
–
22
2
*
–
2
=
5
.
5

????

??????

6
.

6.

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

Substitute x=
6

in equation for y.

??
=
–
2
x
2
+
22
x
+
13
.

–
2
*
6
2
+
22
*
6
+
13
.

–
72+132+13.