Mathematics
Mathematics, 22.09.2019 06:50, YSGabino2991

Question
your assignment: profit from sales
you are deciding how much to charge for an item you want to sell. to answer these questions, you will factor a polynomial expression to find the break-even points, or the prices at which your profit from sales will be 0.
1. circle the item that you want to sell.
t-shirts hats water bottles
making sense of the problem
make sense of the problem
what do you know?
what do you want to find out?
what kind of answer do you expect?
3. fill in the blanks. (1 point)
the profit expression is
4. set the profit expression as an equation equal to 0. (1 point)
= 0
5. factor out the coefficient of the squared term. (2 points)
6. factor the remaining trinomial. (4 points: 2 points for each factor)
7. if a product is equal to 0, then at least one of the factors must be 0. the constant factor cannot be 0. set each binomial factor equal to 0 and solve for the variable. (2 points: 1 point for each factor)
8. use your answer from question 7 to identify the two break-even points. (1 point)
you will make a profit if you sell your item for between $ and $
9. check your work. substitute each value into the equation from question 4 to confirm that it makes the expression equal to 0. (2 points: 1 point for each value)
10. below are the graphs for the profit functions. write the coordinates of the highest point on the graph for your item. (1 point)

11. the x-value of the point from question 10 is the price that will give you the maximum profit. the y-value of the point is the maximum profit that you can make. (3 points)
prompt
transcript: modeling: factoring polynomials
this interactive animation shows an image of a basketball game between two teams. the title "profit from sales" is shown and a "begin" button starts the animation. [click "begin."]
on-screen text and audio:
profit from sales: you're setting up a table at a basketball game to sell items to raise money for the student association. there are costs associated with buying the items. after you pay these costs, the profit, or money you make, will depend on the price the item sells for. you need to decide how much to charge. first, pick an item that you want to sell. [an image of a grey t-shirt, a water bottle, and a black hat can be seen on the screen. any of the images can be clicked and a message pops up.]
t-shirts: great! you've decided to sell t-shirts. the expression –2t2 + 60t – 250 represents your profit when the price of a t-shirt is t dollars.
the break-even points are the prices at which your profit will be 0. write an equation by setting the above expression equal to 0. then factor the expression to find the break-even points for this item.
water bottles: great! you've decided to sell water bottles. the expression –10w2 + 100w – 90 represents your profit when the price of a water bottle is w dollars.
the break-even points are the prices at which your profit will be 0. write an equation by setting the above expression equal to 0. then factor the expression to find the break-even points for this item.
hats: great! you've decided to sell hats. the expression –3h2 + 66h – 120 represents the profit for the hats when the price of a hat is h dollars.
the break-even points are the prices at which your profit will be 0. write an equation by setting the above expression equal to 0. then factor the expression to find the break-even points for this item.


Question your assignment: profit from sales you are deciding how much to charge for an

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your assignment: profit from sales
you are deciding how much to charge for an...

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