SOLUTION: 1. You are planning to Cowboy Hats during the roundup and rodeo season in your town. You are viewing sales of cowboy hats for the previous 10 years to plan your supplies for each d

Question 498884: 1. You are planning to Cowboy Hats during the roundup and rodeo season in your town. You are viewing sales of cowboy hats for the previous 10 years to plan your supplies for each day. You find that the following equation models your sales of cowboy hats each day for the period of time during this season (x = 1 is the day the cowboy hats go on sale):
Cowboy Hats = -0.4x2 + 20x + 10

a. What happens to the sales of cowboy hats as time passes? (10% of grade)

b. Use the Quadratic equation to determine the last day that cowboy hats will be sold. (20% of grade)

c. After how many days will the peak in sales of cowboy hats occur? (20% of grade)

d. How many cowboy hats will be sold on the day the peak occurs? (20% of grade)

e. What will be the coordinates on a graph of the vertex? (10% of grade)

f. How many solutions are there to the equation �-0.4x2 + 20x + 10 = 0� and how do you know this? (10% of grade)

g. What do the solutions in �part f� represent? Do any of the solutions not make sense? Why or why not? (10% of grade)

Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
You do not need to put the "% of grade" because that is irrelevant to us.

Here is a graph of the function (this will answer nearly half of your questions):
http://www.wolframalpha.com/input/?i=f%28x%29+%3D+-.4x^2+%2B+20x+%2B+10

Note that the quadratic formula says that the roots of a quadratic polynomial in the form ax^2 + bx + c are

The x-coordinate of the vertex is equal to the average of the zeros (-b/2a), and the polynomial can be evaluated at that number to obtain the number of cowboy hats sold on that day.

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