Name Date Cleverly Concealed Conics Portfolio Directions: For this portfolio, you will find examples of the four conic sections in the world around you. Once you have examples of each conic section, you will choose one to analyze more closely. You will generate the equation and find the important parts of the conic section. Then you will move the foci and write a paragraph explaining the implications of the move for the application. Finally, you will reflect on your conic exploration. Be sure to complete all four parts of the portfolio before submitting it to your teacher. Part 1: Conic Examples Find real-world examples of each conic section. You may use items or structures in your surroundings, or may search for items on the Internet. Complete the tables for each of your models. Provide as much detail as possible to explain how these are good examples of the conic sections. Be sure to cite your source and provide a photo or a sketch. Record your notes for your example of a circular structure in the following table. Conic: Circle Notes Example Source Photo or Sketch Description of Cleverly Concealed Conic Record your notes for your example of an elliptical structure in the following table. Conic: Ellipse Notes Example © 2016 Connections Education LLC. All rights reserved. Conic: Ellipse Notes Source Photo or Sketch Description of Cleverly Concealed Conic Record your notes for your example of a parabolic structure in the following table. Conic: Parabola Notes Example Source Photo or Sketch Description of Cleverly Concealed Conic Record your notes for your example of a hyperbolic structure in the following table. Conic: Hyperbola Notes Example © 2016 Connections Education LLC. All rights reserved. 2 Conic: Hyperbola Notes Source Photo or Sketch Description of Cleverly Concealed Conic Part 2: Conic Graph and Equation Choose one of your conic examples to study in greater detail. Complete the table to create the graph and equation for your chosen example. 1. If possible, use a photo of the structure or item. Otherwise, draw a detailed sketch. 2. Measure and label the key dimensions of the shape in order to duplicate them in a to-scale graph. Be sure to label your units of measure to reflect the actual measurements. 3. Draw the underlying conic section on a coordinate grid. 4. Identify the coordinates of the appropriate key parts of the conic section. 5. Determine the closest approximation of the equation in standard form for the conic section. Your Conic Section Notes Conic Example © 2016 Connections Education LLC. All rights reserved. 3 Your Conic Section Notes Photo or Sketch This part can be done in a standalone file. Measurements Include the key parts of the chosen conic section. Graph of Conic Section You may use separate grid paper or copy and paste a screenshot or photo of your graph. Equation Use standard form for the conic section you chose. © 2016 Connections Education LLC. All rights reserved. 4 Part 3: A New Graph Double or half the distance from the foci/focus to the vertices/vertex, and determine the new key points on the graph. Calculate what happens to the equation. Compare the new graph to the original graph. Write a paragraph explaining what would happen if your original example were changed in that way. What impact would the shape change have on the function served by the example? New Conic Section Notes Conic Example double or half New Key Points New Equation Graph of Revised Conic You may use separate grid paper or copy and paste a screenshot or photo of your graph. Impact on Real-World Use or Purpose Part 4: Reflection Write a paragraph explaining what you learned about conics and describe any challenges you encountered. © 2016 Connections Education LLC. All rights reserved. 5
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