Modeling with Quadratic Equations

Question 1

The vertex is located at (8.33, 236.67). What does this point represent in context?

Revolt · Accepted Answer

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.

Question 2

What do the zeroes mean in context?

Revolt · Accepted Answer

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

Question 3

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.

Revolt · Accepted Answer

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.

Question 4

Which did you include in your response?

Revolt · Accepted Answer

A: The vertex is the maximum of the graph.; B: The maximum daily profit from the sale of soccer balls is $236.67.; C: The maximum profit occurs when the store charges $8.33 per soccer ball.

Question 5

What are the zeroes of the function? Round to the nearest hundredth.

Revolt · Accepted Answer

B: 2.05; D: 14.61

Question 6

Which did you include in your response?

Revolt · Accepted Answer

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Modeling with Quadratic Equations Answers

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