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# Finding a quadratic equation given zeros and start-up costs?

I need help finding the equation.

A new coffe franchise has been opened and the owner wants to determine a quadratic relation that will model the profit he is able to make based upon the number of customers who visit his store. He knows that his start up costs are $250 000, and that he will break even if either 5,000 or 10,000 customers visit his store.

a) determine the quadratic relation that models this situation. Use "P" for profit ( in thousands $) and "n" for the number of customers (in thousands).

I found P=(x-5)(x-10) but the answer is P= -5(x-5)(x-10)... where do we get the negative 5? ;_;

### 1 Answer

- I'm with StupidLv 79 years agoFavorite Answer
you are given two zeros, and a third point on the curve

so use intercept form:

P = a(x - 5)(x - 10)

given point is (0, -250)

because if no one shows up, he loses 250k.

then plug in given point to find a:

-250 = a(0 - 5)(0 -10)

-250 = 50a

a = -5

and so

P = -5(x - 5)(x - 10)

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