AnswersFL-1200330-Algebra 2 AThe Quadratic Formula

The Quadratic Formula Answers

7 verified answers6 views
1
Free Preview

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?

Question illustration
A
If the store sells more soccer balls, they can decrease the price.
B
If the soccer balls are returned for a refund, the store will lose money.
C
If the soccer balls are too expensive, fewer will be sold, reducing profit.
2
Free Preview

What do the zeroes mean in context?

A
If soccer balls are sold for $2.05 each, the store will make a daily profit of $14.61.
B
If soccer balls are sold for $14.61 each, the store will make a daily profit of $2.05.
C
If soccer balls are sold for $2.05 or $14.61 each, the store will maximize their daily profit.
D
If soccer balls are sold for $2.05 or $14.61 each, the store will break even but will not make a profit.
3

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

A
If the store charges $5 per soccer ball, it can expect to sell 170 of them.
B
If the store charges $8 per soccer ball, it makes a daily profit of $236.
C
If the store sells 12 soccer balls, it makes $156 in profit.
D
The greater the selling price, the greater the profit.
4

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

A
(16.67, 1,306.67)
B
(8.33, 236.67)
C
(0.03, –177)
D
(8.33,0)
E
(2, 0)
F
(14.61, 0)
5

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

A
0
B
2.05
C
8.33
D
14.61
6

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.

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.

7

Sample Response: 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. Which did you include in your response?the equation 150 = –6x2 + 100x – 180zeroes at 4.53 and 12.13the price of soccer balls that will result in $150 daily profit

A
the equation 150 = –6x2 + 100x – 180
B
zeroes at 4.53 and 12.13
C
the price of soccer balls that will result in $150 daily profit

Did you find these answers helpful?

More from this Course

Assignment
30 verified answers

Transformations of Quadratic Functions

Assignment
36 verified answers

The Quadratic Formula

Assignment
29 verified answers

Lesson 6: The Quadratic Formula