Question

A company plans to sell a new type of vacuum cleaner for $280 each. The company’s financial planner estimates that the cost, y, of manufacturing the vacuum cleaners is a quadratic function with a y-intercept of 11,000 and a vertex of (500, 24,000). Which system of equations can be used to determine how many vacuums must be sold for the company to make a profit?



$A.\left \{ {{y=280x} \atop {x=-0.052(x-500)^2+24000}} \right.$
$B. \left \{ {{y=280x} \atop {y=0.052x^2+11,000}} \right.$
$C. \left \{ {{y=280x} \atop {y=0.052(x-500)^2+24000}} \right.$
$D. \left \{ {{y=280x} \atop {x=-0.052(x-500)^2+11000}} \right.$

Answer 1

Suppose x is vaccuums sold, $280 each vaccum, 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 how many vacuums must be sold for the company to make a profit.

Answer 2

Answer:

A.     y=280x

x=-0.052x^2+11,000

This is correct for the genuity of Edg :)