A company plans to sell a new type of cleaner for $280 each. The estimated cost, y, of manufacturing the cleaners is a function with a y-int of 11,000 and a vertex of (500, 24,000). How many must be sold for the company to make a profit?

Suppose x is sold, $280 each, and y is the total financial cost. The first equation in the system is then certainly y = 280x.

The vertex form y-k = a (x-h) ^2 where (h, k) is the vertex, and y is the y-intercept.

So, plug the values in.

11,000-24,000 = a (0-500) ^2

-13,000=250,000a

a=-0.052

y - 24,000 = - 0.052 (x-500) ^2

y = - 0.052 (x-500) ^2 + 24,000

This is the second equation in the system.

The answer is then A, which contain the system of equations which can be used to determine must be sold for the company to make a profit.