The vertex is located at (8.33, 236.67). What does this point represent in context?
The vertex represents the maximum point of the quadratic function. In context, the x-coordinate (8.33) represents the price per soccer ball that will result in the maximum profit, and the y-coordinate (236.67) represents the maximum daily profit of $236.67.
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What do the zeroes mean in context?
Suppose the store wants to earn a daily profit of $150 from the sale of soccer balls. To earn this profit, what price should the store charge for each soccer ball? Explain how to solve this problem.
To find the price that results in a daily profit of $150, set the profit equation equal to 150: 150 = -6x² + 100x - 180. Subtract 150 from both sides to get -6x² + 100x - 330 = 0. Using the quadratic formula, the solutions for x (the price) are approximately $4.53 and $12.13. Therefore, the store should charge either $4.53 or $12.13 per soccer ball to earn a $150 profit.
What are the zeroes of the function? Round to the nearest hundredth.
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