Modeling with Quadratic Equations

Question 1

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

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

Question 2

What do the zeroes mean in context?

Revolt · Accepted Answer

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

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

Revolt · Accepted Answer

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

(8.33, 236.67)

Question 5

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

Revolt · Accepted Answer

2.05; 14.61

Question 6

Soccer balls go on sale for $7.50 each. The store also sells footballs and the manager wants to earn a daily profit of $400 from both items. The equation models the store’s daily profit, y, for selling footballs at x dollars. Explain how to find the price per football needed to meet the goal.

Revolt · Accepted Answer

At $7.50 per soccer ball, they earn a daily profit of $232.50. The store needs to earn a daily profit of $400 – $232.50 = $167.50 from footballs. Solve 167.50 = –4x2 + 80x – 150 to find the price for footballs: x = $5.46 and $14.54.

Question 7

The quadratic equation y = –6x2 + 100x – 180 models the store’s daily profit, y, for selling soccer balls at x dollars.The quadratic equation y = –4x2 + 80x – 150 models the store’s daily profit, y, for selling footballs at x dollars. Use a graphing calculator to find the intersection point(s) of the graphs, and explain what they mean in the context of the problem.

Revolt · Accepted Answer

points of intersection represent when the price and profit are the same for each type of ball. The intersection points are approximately(8.16, 236.49) and (1.84, –16.49). When the store charges $8.16 for each type of ball, they make the same profit from each ball, approximately $236.49. Charging $1.88 provides no profit for either type of ball.

Question 8

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 9

Which did you include in your response?

Revolt · Accepted Answer

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

Question 10

Which did you include in your response?

Revolt · Accepted Answer

Solve 167.50 = –4x2 + 80x – 150 to find the price for footballs: x = $5.46 and $14.54.

Modeling with Quadratic Equations Answers

More from this Course

TRY EDGENUITY HACKS