AnswersFL-1200330-Algebra 2 CRModeling with Quadratic Equations

Modeling with Quadratic Equations Answers

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1
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What are the zeroes of the function? Round to the nearest hundredth.

A
0
B
2.05
C
8.33
D
14.61
2
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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

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.
4

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.
5

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)
6

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.
7

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.
8

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)
9

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

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.

10

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

A
0
B
2.05
C
8.33
D
14.61
11

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:

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.

12

Which did you include in your response?

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.
13

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.
14

Which did you include in your response?

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

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