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? StartLayout Enlarged Left-Brace 1st Row y = 280 x 2nd Row y = negative 0.052 (x minus 500) squared + 24,000 EndLayout

StartLayout Enlarged Left-Brace 1st Row y = 280 x 2nd Row y = 0.052 x squared + 11,000 EndLayout

StartLayout Enlarged Left-Brace 1st Row y = 280 x 2nd Row y = 0.052 (x minus 500) squared + 24,000 EndLayout

StartLayout Enlarged Left-Brace 1st Row y = 280 x 2nd Row y = negative 0.052 (x minus 500) squared + 11,000 EndLayout

StartLayout Enlarged Left-Brace 1st Row y = 280 x 2nd Row y = negative 0.052 (x minus 500) squared + 24,000 EndLayout

Step-by-step explanation:

Given that:

Cost per cleaner = $280

The cost of x vacuum cleaners will be :

Cost per cleaner * number of cleaners

$280 * x

= $280x

The general vertex firm equation :

y-k = a(x-h)^2

Vertex = (500, 24000) ; Vertex = (h, k)

h = 500 ; k =24000 y= 11000, x = 0

y intercept = 11000

Plugging the values :

11000 - 24000 = a(0 - 500)^2

- 13000 = a(-500)^2

-13000 = a * 250000

a = - 13000 / 250000

a = - 0.052

Hence,

y - 24000 = a(0 - 500)^2

y = - 0.052(0 - 500)^2 + 24000

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