Question

PLZ HELP!!!!!!!!!!!!!!!!!!

Y=-6x^2+100x-180. What do the zeroes mean in context?

A.) If soccer balls are sold for $2.05 each, the store will make a daily profit of $14.61
B.) If soccer balls are sold for $14.61 each, the store will make a daily profit of $2.05.
C.) If soccer balls are sold for $2.05 or $14.61 each, the store will maximize their daily profit.
D.) If soccer balls are sold for $2.05 or $14.61 each, the store will break even but will not make a profit.

Answer 1

If soccer balls are sold for $2.05 or $14.61 each, the store will break even but will not make a profit.

Answer 2

D.) If soccer balls are sold for $2.05 or $14.61 each, the store will break even but will not make a profit.

Explanation:

Let us assume x = selling price of each soccer ball

y = daily profit earned from selling of soccer balls

Given that

Y=
`-6x^2+100x-180`

where,

a = -6

b = 100

c = -180

Now we have to applied the formula which is as follows

x
`= (-b\pm√(b^2-4ac))/(2a)$`

`= (-100\pm√(100^2-4* -6* -180))/(2* -6)$`

`= (-100\pm√(10,000 - 4,320))/(-12)$`

`= (-100\pm√(5.680))/(-12)$`

`= (-100 + 75.3658)/(-12)$`

`= (24.6342)/(-12)`

x^1 = -2.05285

Now

x^2
`= (-100 - 75.3658)/(-12)$`

`= (- 175.3658)/(-12)`

x^2 = 14.6138

Based on this the option D is most appropriate as per the given situation