SOLUTION: I have the first three parts of the question figured out but once I hit 1c.I get lost after solving using the quadratic formula. 1.Suppose you are an event coordinator for a larg

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Question 633539: I have the first three parts of the question figured out but once I hit 1c.I get lost after solving using the quadratic formula.
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. (x=1 is the day tickets go on sale).
tickets=-0.1x^2+12x+11
1a.Does the graph of this equation open up or down? How did you determine this?The graph opens downward. I determined this by looking at the coefficient of the variable x, which was -0.1. Since the coefficient of the variable is negative, it opens downward, if the coefficient of the variable x were positive it point upward. (how do I prove this?Is there some equation I need to throw in?)
1b.Describe what happens to the tickets sales as time passes.
The ticket sales will initially raise but then they will peak and eventually fall to zero as time passes.
1c.Use the quadratic equation to determine the last day that tickets will be sold.
x=120.9098,-0.9098
I think it's after the 121st day tickets will stop being sold.
I am lost here after...
1d. Will tickets peak or be at a low during the middle of the sale? How do you know?
1e. After how many days will the peak or low occur?
1f. How many tickets will be sold on the day when the peak or low occurs?
1g.What is the point of the vertex? How does this number relate to your answers in parts e. and f?
1h.How many solutions are there to the equation ? How do you know?
I need to show work on everything...
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!
 

Hi,

Re TY, having found the Vertex(60,371) by completing the Square, we know that is a Max Pt

tickets= -0.1x^2+12x+11  =    | Completing the Square

Note: the vertex form of a Parabola opening up(a>0) or down(a<0),  

where(h,k) is the vertex  

 Opens down and vertex is (60,371), the Peak sold on one day is 371 tickets on day 60.  

|Sales increasing up to 60 days and then decreasing

 

     (x-60)^2 = 3710

       x = 60 + sqrt(3710) is the last day tikets will be sold. on the 121st day 



 

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