Expert: Scott A Wilson - 6/13/2010

Question
I just don't understand I keep gtting stuck I just want to get it right, but it has been difficult for me with quadratic equATIONS. It is not allowing me to attach!!

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 -0.2x^2+14x+11

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.How many solutions are there to the equation -0.2x^2+14x+11=0
How can you determine without solving the quadratic equation for x?
D.Use the quadratic formula to solve the equation -0.2x^2+14x+11=0
E.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?
F.What is the last day that tickets will be sold?  Hint: Review the answer of #1d.
Note. Write your answer in terms of the number of days after ticket sales begin.
G.Will tickets peak or be at a low during the middle of the sale? How do you know?
H.After how many days will the peak or low occur?  How can you calculate the value?
I.How many tickets will be sold on the day when the peak or low occurs?
J.What is the point of the vertex? Hint: A point has two coordinates (x, y).How does this number relate to your answers in parts e. and f?

I will really appreciate if you could help me out, I know it goes downward on the graph.

Answer
A.Does the graph of this equation open up or down? How did you determine this?
The equation is of the form Ax² + Bx + C; it goes up if A is positive and down if A is negative.

B.Describe what happens to the tickets sales as time passes.
At first they go up, then they go down.

C.How many solutions are there to the equation -0.2x^2+14x+11=0
Since it is a quadratice equation (has power 2), there are at most 2 solutions;
to check this, remember the quadratic equation is (-b±√(b²-4ac)/(2a), so if b²-4ac is positive, there are 2 solutions; if it is negative, there are no solutions; if it is 0, there is one solution.

How can you determine without solving the quadratic equation for x?
To determine how many roots there are, look at the sign of b²-4ac.

D.Use the quadratic formula to solve the equation -0.2x^2+14x+11=0
Use quadratic formula given with a = -0.2, b = 14, and c = 11.

E.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?
There are two roots, but one is negative, which in time, makes no sense.

F.What is the last day that tickets will be sold?  Hint: Review the answer of #1d.
Note. Write your answer in terms of the number of days after ticket sales begin.
To find the last day, look at the values in Excel.  It can be seen the when x gets up to somewhere around 70, the answer becomes negative.

G.Will tickets peak or be at a low during the middle of the sale? How do you know?
They will be at a max since the parabola opens downward.

H.After how many days will the peak or low occur?  How can you calculate the value?
The peak will be near half of the date when they go negative.  That is since parabolas are symmetric.

I.How many tickets will be sold on the day when the peak or low occurs?
Somewhere over 250 tickets will be sold around the 35th day.
Try in the mid 30's to see where maximum is.

J.What is the point of the vertex?  Hint: A point has two coordinates (x, y).
How does this number relate to your answers in parts e. and f?
The vertex is where the maximum occurs.