# Robert Lindblom Math & Science Academy

. Name: ________________________________ Date: _________ Period: __________

Quadratic Functions Project: Parabolas Everywhere

Objective: Why are we assigning this to you?

1) To recognize and identify parabolas in everyday life.

2) To model objects with parabolic shape with quadratic equations

Instructions: What you have to do!

1. Find 4 examples of the graph of a quadratic function with a camera anywhere around the city.

a. Your photos need to have an indentifying feature so I know you took the photo. Example: drawing a smile face on your finger with your initials and having it in the photo.

2. Choose 1 of your photos and draw a coordinate graph system over the picture. You may do this with tracing paper, graph paper, or on the computer. Mark the scale clearly.

a. You may need to enlarge the quadratic part of the artwork to draw a set of coordinate axes. If so, please include a copy of the original work of art or architecture as well

3. Find the coordinates of five points on your graph and place these five points on a clearly labeled table. Show your function fits by checking a 6th point.

4. Find the quadratic function that best models your image without the use of a regression.

a. To score highly you will need to explain in your report the steps you took to model this image with a quadratic function.

5. Write up your project in a REPORT section on your poster and to help we provided an example. Simply following the example is the Minimum and will earn a B but the quality and extension of each question can earn an A.

6. Discuss your project with the class in a 3 – 5 minute presentation. Make sure that your poster/paper includes at least 3 interesting facts related to your image you choose and has the other images you explored.

7. ** This project may be done electronically. You may capture images and map a quadratic equation to the screen. See at 1:00 minute for example.

Other information:

• All work will be completed outside of school.

• This project is to be completed independently. No two students can use the same piece of artwork/architecture or picture.

• WARNING!!! Some pictures may appear to be parabolas but may not actually be real parabolas. If your artwork is not a true parabola, but is close, please make sure that you state that in your project and presentation. Discuss the amount of error from a true parabola. (i.e St. Louis Arch)

Project Timeline

• M/T, 3/10-3/11: Project Assigned

• M/T, 3/17-3/18: Photos completed and brought to class for 15 points class participation

• M/T, 3/24 – 3/25: Last day to get help from Mr. Morrison

• Th/F, 3/27 - 3/28: Project due / presentation day in class.

Name: __________________________________ Date: ________________ Period: _______

Project Idea Submission Form

(Submit this rubric to teacher on presentation day 3/27 or 3/28)

Description of photo: _________________________________________________

Source: (where did you find it? )__________________________________________________

Project Title: ____________________________________________________

Use the following rubric as a “checklist” to help you as you complete your project. It will be used to score your project.

Rubric:

|Criteria |Points possible |Points earned |

|4 original pictures of parabolas, without the coordinate |5 | |

|plane included. | | |

|A coordinate graph was accurately drawn and labeled over a |10 | |

|copy of 1 parabola. An accurate scale was included on the | | |

|graph, showing the relationship between the picture size and| | |

|the actual size of the parabola. | | |

|5 points, including the vertex, were accurately labeled on |10 | |

|the graph of the parabola. | | |

|A quadratic equation was accurately found and included in |15 | |

|vertex form and standard form. | | |

|Work was shown to use the quadratic equation to calculate |10 | |

|the y-coordinate for the x-coordinate of one of the 5 | | |

|labeled points. Discussion included why or why not the | | |

|calculated y-value matched the labeled y-coordinate (see | | |

|example for guidance). | | |

|Report was well written to include how student found an |30 | |

|appropriate a, h, k. Please use the example as a guide to | | |

|the quality of answers in the report. | | |

|Results were presented in a well written, neat, and |10 | |

|organized poster. | | |

|Poster included at least 3 interesting facts about the photo| | |

|and has all sections of poster clearly labeled. | | |

|Presentation was clear, engaging, and between 3 -5 minutes |10 | |

|in length. Discussion of a, h, and k along with other | | |

|aspects of quadratic functions were clear and accurate. At | | |

|least 3 interesting facts were discussed during the | | |

|presentation. | | |

|Total |100 points | |

Example Project

The Eiffel Tower in Paris, France

Full size image:

[pic]

Source:

Example Project

The Eiffel Tower in Paris, France

Enlarged Image:

[pic]

Source:

3 Interesting facts:

• The Eiffel tower is 986 feet tall and is constructed out of iron material.

• The Eiffel Tower was built in 1889 and was the tallest structure in the world until 1930.

• The tower was named after its designer and engineer, Gustave Eiffel, and over 5.5 million people visit the tower every year.

Source:

Coordinate Plane:

Actual height: 986 ft tall 986/19 (

Height in this picture: 19 cm

Finding the Quadratic Regression:

Report

I chose 5 points on the graph with the following coordinates:

Point A: (-4, 4)

Point B: (-3, 5)

Point C: (1, 6)

Point D: (3, 5)

Point E: (5, 3)

I used these 5 points to guide my creation of a quadratic equation. I found the following approximate equation by first plotting just the points on a graph.

[pic] (screen shots not required)

These points look like they would fit on a quadratic function that faces down so I tried to graph the parent function with a negative coefficient. But that looks far off so I…

[pic] (screen shots not required)

Tried to shit the vertex up the y-axis to have it match where I thought the vertex would be. It looks like it should near the y axis and around 6 units up. So I added a “k” value of 6.1 to the negative parent function.

[pic]

Well that got my function up there but I think the vertex is more to the right so I added an “h” value of 0.2 so I could shift the function to the right.

[pic]

Now the picture is still off and I know it needs to be wider so I changed the “a” value to a number very close to zero but negative. I chose 1/8 because it is small and a nice fraction and the calculator changed it to a decimal. I also changed my “h” value back to zero since that matched better to my data. Now this looks right so my final equation is …

[pic]

-----------------------

y

Prediction point tested in the regression equation

C

D

B

E

A

x

-6 -4 -2 0 2 4 6 8

Scale:

1 cm = 51.9 ft

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