Expert answer:Honors Project Comparing Functions
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Math | Graded Assignment | Honors Project: Modeling with Polynomials
Name:
Date:
Graded Assignment
Honors Project: Modeling with Polynomials
You work for the BeeSwaks Candle Company and have been asked to update two of the company’s earliest
candle designs, the Brick and the Egyptian. The original Brick was a cube 8 centimeters on a side. The original
Egyptian was a pyramid 21 centimeters tall with a square base 10 centimeters on a side.
Improvements in the manufacturing process have made it possible to change the design of these candles for a
fresh new look and improved profit. You have been asked to work within the following guidelines:
Name
The Brick
The Egyptian
Shape
rectangular prism
right square pyramid
Base
dimensions can vary;
but it must be a square
same dimensions as
base of the Brick
Height
1 cm less than the side
length of the base
21 cm
You are preparing for a meeting with BeeSwaks executives in which they will make decisions about the how many
candles to make, final design details, and retail prices for each candle.
Answer the questions below. When you are finished, submit this to your teacher by the due date for full credit.
Total score: ____ of 30 points
© 2015 K12 Inc. All rights reserved.
Copying or distributing without K12’s written consent is prohibited.
Page 1 of 4
Math | Graded Assignment | Honors Project: Modeling with Polynomials
(Score for Question 1: ___ of 12 points)
1. Create a labeled diagram of the Brick. Use x to represent the length of a side of the base of the candle. Then
write an equation for the volume of the candle in terms of x. Write the polynomial in standard form.
Answer:
© 2015 K12 Inc. All rights reserved.
Copying or distributing without K12’s written consent is prohibited.
Page 2 of 4
Math | Graded Assignment | Honors Project: Modeling with Polynomials
(Score for Question 2: ___ of 12 points)
2. Create a labeled diagram of the Egyptian. Use x to represent the length of a side of the base of the candle.
Then write an equation for the volume of the candle in terms of x. Write the polynomial in standard form.
Answer:
© 2015 K12 Inc. All rights reserved.
Copying or distributing without K12’s written consent is prohibited.
Page 3 of 4
Math | Graded Assignment | Honors Project: Modeling with Polynomials
(Score for Question 3: ___ of 6 points)
3. To impress management, you decide to propose your own original candle design based on solid figures.
Make your candle design attractive but also make sure it will be practical to manufacture. Draw the candle in
the space below and label the drawing with dimensions. Then write an equation for the volume of the candle
in terms of x, where x is a dimension that defines the area of the candle’s base. Write the polynomial in
standard form.
Answer:
© 2015 K12 Inc. All rights reserved.
Copying or distributing without K12’s written consent is prohibited.
Page 4 of 4
Math | Graded Assignment | Honors Project: Modeling with Polynomials
Name:
Date:
Graded Assignment
Honors Project: Modeling with Polynomials
You work for the BeeSwaks Candle Company and have been asked to update two of the company’s earliest
candle designs, the Brick and the Egyptian. The original Brick was a cube 8 centimeters on a side. The original
Egyptian was a pyramid 21 centimeters tall with a square base 10 centimeters on a side.
Improvements in the manufacturing process have made it possible to change the design of these candles for a
fresh new look and improved profit. You have been asked to work within the following guidelines:
Name
The Brick
The Egyptian
Shape
rectangular prism
right square pyramid
Base
dimensions can vary;
but it must be a square
same dimensions as
base of the Brick
Height
1 cm less than the side
length of the base
21 cm
You are preparing for a meeting with BeeSwaks executives in which they will make decisions about the how many
candles to make, final design details, and retail prices for each candle.
Answer the questions below. When you are finished, submit this to your teacher by the due date for full credit.
Total score: ____ of 30 points
© 2015 K12 Inc. All rights reserved.
Copying or distributing without K12’s written consent is prohibited.
Page 1 of 4
Math | Graded Assignment | Honors Project: Modeling with Polynomials
(Score for Question 1: ___ of 12 points)
1. Create a labeled diagram of the Brick. Use x to represent the length of a side of the base of the candle. Then
write an equation for the volume of the candle in terms of x. Write the polynomial in standard form.
Answer:
© 2015 K12 Inc. All rights reserved.
Copying or distributing without K12’s written consent is prohibited.
Page 2 of 4
Math | Graded Assignment | Honors Project: Modeling with Polynomials
(Score for Question 2: ___ of 12 points)
2. Create a labeled diagram of the Egyptian. Use x to represent the length of a side of the base of the candle.
Then write an equation for the volume of the candle in terms of x. Write the polynomial in standard form.
Answer:
© 2015 K12 Inc. All rights reserved.
Copying or distributing without K12’s written consent is prohibited.
Page 3 of 4
Math | Graded Assignment | Honors Project: Modeling with Polynomials
(Score for Question 3: ___ of 6 points)
3. To impress management, you decide to propose your own original candle design based on solid figures.
Make your candle design attractive but also make sure it will be practical to manufacture. Draw the candle in
the space below and label the drawing with dimensions. Then write an equation for the volume of the candle
in terms of x, where x is a dimension that defines the area of the candle’s base. Write the polynomial in
standard form.
Answer:
© 2015 K12 Inc. All rights reserved.
Copying or distributing without K12’s written consent is prohibited.
Page 4 of 4
Math | Graded Assignment | Honors Project: Modeling with Polynomials
Name:
Date:
Graded Assignment
Honors Project: Modeling with Polynomials
You work for the BeeSwaks Candle Company and have been asked to update two of the company’s earliest
candle designs, the Brick and the Egyptian. The original Brick was a cube 8 centimeters on a side. The original
Egyptian was a pyramid 21 centimeters tall with a square base 10 centimeters on a side.
Improvements in the manufacturing process have made it possible to change the design of these candles for a
fresh new look and improved profit. You have been asked to work within the following guidelines:
Name
The Brick
The Egyptian
Shape
rectangular prism
right square pyramid
Base
dimensions can vary;
but it must be a square
same dimensions as
base of the Brick
Height
1 cm less than the side
length of the base
21 cm
You are preparing for a meeting with BeeSwaks executives in which they will make decisions about the how many
candles to make, final design details, and retail prices for each candle.
Answer the questions below. When you are finished, submit this to your teacher by the due date for full credit.
Total score: ____ of 30 points
© 2015 K12 Inc. All rights reserved.
Copying or distributing without K12’s written consent is prohibited.
Page 1 of 4
Math | Graded Assignment | Honors Project: Modeling with Polynomials
(Score for Question 1: ___ of 12 points)
1. Create a labeled diagram of the Brick. Use x to represent the length of a side of the base of the candle. Then
write an equation for the volume of the candle in terms of x. Write the polynomial in standard form.
Answer:
© 2015 K12 Inc. All rights reserved.
Copying or distributing without K12’s written consent is prohibited.
Page 2 of 4
Math | Graded Assignment | Honors Project: Modeling with Polynomials
(Score for Question 2: ___ of 12 points)
2. Create a labeled diagram of the Egyptian. Use x to represent the length of a side of the base of the candle.
Then write an equation for the volume of the candle in terms of x. Write the polynomial in standard form.
Answer:
© 2015 K12 Inc. All rights reserved.
Copying or distributing without K12’s written consent is prohibited.
Page 3 of 4
Math | Graded Assignment | Honors Project: Modeling with Polynomials
(Score for Question 3: ___ of 6 points)
3. To impress management, you decide to propose your own original candle design based on solid figures.
Make your candle design attractive but also make sure it will be practical to manufacture. Draw the candle in
the space below and label the drawing with dimensions. Then write an equation for the volume of the candle
in terms of x, where x is a dimension that defines the area of the candle’s base. Write the polynomial in
standard form.
Answer:
© 2015 K12 Inc. All rights reserved.
Copying or distributing without K12’s written consent is prohibited.
Page 4 of 4
Math | Graded Assignment | Honors Project: Modeling with Polynomials
Name:
Date:
Graded Assignment
Honors Project: Modeling with Polynomials
You work for the BeeSwaks Candle Company and have been asked to update two of the company’s earliest
candle designs, the Brick and the Egyptian. The original Brick was a cube 8 centimeters on a side. The original
Egyptian was a pyramid 21 centimeters tall with a square base 10 centimeters on a side.
Improvements in the manufacturing process have made it possible to change the design of these candles for a
fresh new look and improved profit. You have been asked to work within the following guidelines:
Name
The Brick
The Egyptian
Shape
rectangular prism
right square pyramid
Base
dimensions can vary;
but it must be a square
same dimensions as
base of the Brick
Height
1 cm less than the side
length of the base
21 cm
You are preparing for a meeting with BeeSwaks executives in which they will make decisions about the how many
candles to make, final design details, and retail prices for each candle.
Answer the questions below. When you are finished, submit this to your teacher by the due date for full credit.
Total score: ____ of 30 points
© 2015 K12 Inc. All rights reserved.
Copying or distributing without K12’s written consent is prohibited.
Page 1 of 4
Math | Graded Assignment | Honors Project: Modeling with Polynomials
(Score for Question 1: ___ of 12 points)
1. Create a labeled diagram of the Brick. Use x to represent the length of a side of the base of the candle. Then
write an equation for the volume of the candle in terms of x. Write the polynomial in standard form.
Answer:
© 2015 K12 Inc. All rights reserved.
Copying or distributing without K12’s written consent is prohibited.
Page 2 of 4
Math | Graded Assignment | Honors Project: Modeling with Polynomials
(Score for Question 2: ___ of 12 points)
2. Create a labeled diagram of the Egyptian. Use x to represent the length of a side of the base of the candle.
Then write an equation for the volume of the candle in terms of x. Write the polynomial in standard form.
Answer:
© 2015 K12 Inc. All rights reserved.
Copying or distributing without K12’s written consent is prohibited.
Page 3 of 4
Math | Graded Assignment | Honors Project: Modeling with Polynomials
(Score for Question 3: ___ of 6 points)
3. To impress management, you decide to propose your own original candle design based on solid figures.
Make your candle design attractive but also make sure it will be practical to manufacture. Draw the candle in
the space below and label the drawing with dimensions. Then write an equation for the volume of the candle
in terms of x, where x is a dimension that defines the area of the candle’s base. Write the polynomial in
standard form.
Answer:
© 2015 K12 Inc. All rights reserved.
Copying or distributing without K12’s written consent is prohibited.
Page 4 of 4
Math | Graded Assignment | Honors Project: Comparing Functions
Name:
Date:
Graded Assignment
Honors Project: Comparing Functions
Total score: ____ of 50 points
(Score for Question 1: ___ of 12 points)
1. Use your equations from Lesson 1 for the Brick Candle and the Egyptian Pyramid Candle to create a graph of
two polynomial functions so that you can compare volumes for different values of x. Compare the volumes.
Answer:
© 2015 K12 Inc. All rights reserved.
Copying or distributing without K12’s written consent is prohibited.
Page 1 of 3
Math | Graded Assignment | Honors Project: Comparing Functions
(Score for Question 2: ___ of 8 points)
2. Use the graph from Question 1 to identify where the volumes are equal. Confirm this value by writing and
solving an equation that describes the difference between the volumes of the candle types.
Answer:
© 2015 K12 Inc. All rights reserved.
Copying or distributing without K12’s written consent is prohibited.
Page 2 of 3
Math | Graded Assignment | Honors Project: Comparing Functions
(Score for Question 3: ___ of 30 points)
3. The same wax will be used to make each candle, and it costs 3 of a penny per cubic centimeter. Write
4
polynomial functions to show the cost of the wax that is used for making each candle for different values of x.
Graph the functions. Discuss the costs.
Answer:
© 2015 K12 Inc. All rights reserved.
Copying or distributing without K12’s written consent is prohibited.
Page 3 of 3
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