Modeling with Quadratic Equations

Question 1

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

Revolt · Accepted Answer

B: 2.05; D: 14.61

Question 2

A sporting goods store uses quadratic equations to monitor the daily cost and profit for various items it sells. The store’s daily profit, y, when soccer balls are sold at x dollars each, is modeled by . Why is there an interval over which the graph decreases?

Revolt · Accepted Answer

C: If the soccer balls are too expensive, fewer will be sold, reducing profit.

Question 3

The table shows some values that satisfy the quadratic equation. Which of the following is a true statement?

Revolt · Accepted Answer

B: If the store charges $8 per soccer ball, it makes a daily profit of $236.

Question 4

What is the vertex of the parabola? Round to the nearest hundredth.

Revolt · Accepted Answer

B: (8.33, 236.67)

Question 5

A sporting goods store uses quadratic equations to monitor the daily cost and profit for various items it sells. The store’s daily profit, y, when soccer balls are sold at x dollars each, is modeled by . Why is there an interval over which the graph decreases?

Revolt · Accepted Answer

C: If the soccer balls are too expensive, fewer will be sold, reducing profit.

Question 6

The table shows some values that satisfy the quadratic equation. Which of the following is a true statement?

Revolt · Accepted Answer

B: If the store charges $8 per soccer ball, it makes a daily profit of $236.

Question 7

What is the vertex of the parabola? Round to the nearest hundredth.

Revolt · Accepted Answer

B: (8.33, 236.67)

Question 8

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

Revolt · Accepted Answer

The vertex is the maximum of the graph. The y-coordinate of the maximum is 236.67, which means the greatest possible daily profit from the sale of soccer balls is $236.67. This maximum profit occurs when x = 8.33, or when the store charges $8.33 per soccer ball.

Question 9

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

Revolt · Accepted Answer

B: 2.05; D: 14.61

Question 10

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

need to solve the equation 150 = -6x2 + 100x - 180. I can subtract 150 from both sides and use the quadratic formula to find x = 4.53 and 12.13. This means that if the store sells soccer balls for $4.53 or $12.13, it will earn a daily profit of $150.

Modeling with Quadratic Equations Answers

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