y = -6x^2 + 100x - 180\nx = selling price of each soccer ball\ny = daily profit from soccer balls\nwhat are…

y = -6x^2 + 100x - 180\nx = selling price of each soccer ball\ny = daily profit from soccer balls\nwhat are the zeroes of the function? round to the nearest hundredth.\n0\n2.05\n8.33\n14.61\nwhat do the zeroes mean in context?\nif soccer balls are sold for $2.05 each, the store will make a daily profit of $14.61.\nif soccer balls are sold for $14.61 each, the store will make a daily profit of $2.05.\nif soccer balls are sold for $2.05 or $14.61 each, the store will maximize their daily profit.\nif soccer balls are sold for $2.05 or $14.61 each, the store will break even but will not make a profit.

y = -6x^2 + 100x - 180\nx = selling price of each soccer ball\ny = daily profit from soccer balls\nwhat are the zeroes of the function? round to the nearest hundredth.\n0\n2.05\n8.33\n14.61\nwhat do the zeroes mean in context?\nif soccer balls are sold for $2.05 each, the store will make a daily profit of $14.61.\nif soccer balls are sold for $14.61 each, the store will make a daily profit of $2.05.\nif soccer balls are sold for $2.05 or $14.61 each, the store will maximize their daily profit.\nif soccer balls are sold for $2.05 or $14.61 each, the store will break even but will not make a profit.

Answer

Explanation:

Step1: Recall zero - definition

The zeroes of a function $y = f(x)$ are the values of $x$ for which $y = 0$. So we set $y=-6x^{2}+100x - 180=0$.

Step2: Use quadratic formula

For a quadratic equation $ax^{2}+bx + c = 0$ ($a=-6$, $b = 100$, $c=-180$), the quadratic formula is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. First, calculate the discriminant $\Delta=b^{2}-4ac=(100)^{2}-4\times(-6)\times(-180)=10000 - 4320 = 5680$. Then $x=\frac{-100\pm\sqrt{5680}}{-12}=\frac{-100\pm75.37}{-12}$.

Step3: Find two solutions

$x_1=\frac{-100 + 75.37}{-12}=\frac{-24.63}{-12}\approx2.05$ and $x_2=\frac{-100 - 75.37}{-12}=\frac{-175.37}{-12}\approx14.61$. In the context of profit - function, when $y = 0$, the store breaks even (has no profit or loss).

Answer:

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