Roller Coaster Worksheet

Name:

Partner’s Name:
(leave blank if working alone)

Part 1: Complete Independently

Use any graphing technology of your choice and answer the following questions about your observations. Please use complete sentences.

Scenario 1:

  1. Graph y = –2x2+ 6. Describe what you see.
  2. –2x2+ 6 is what kind of polynomial? Classify the polynomial by degree and number of terms.
  3. Next, graph y =x2+ 6. Describe what you see. How is what you observe here different from what you observed in part A?
  4. If you wanted a really steep hill for your roller coaster, would you use the graph of y = –2x2+ 6 or
    y =x2+ 6?

Scenario 2:

  1. Graph y = x3– 2x2+ 6. Describe what you see.
  2. x3– 2x2+ 6 is what kind of polynomial? Classify the polynomial by degree and number of terms.
  3. Next, graph y = x3– 4x2+ 6. Describe what you see. How is what you observe here different from what you observed in part A?
  4. If you wanted the middle part of your roller coaster to have a steeper drop, would you use the graph of
    y = x3– 2x2+ 6 or y = x3– 4x2+ 6?

Part 2: Complete Independently or with a Partner

  1. Contact your partner if you are choosing to do this project collaboratively. Look at the polynomial below.
    y = ax3+ bx2+ cx + d
    Graph this using any graphing technology of your choice. However, replace the variables a, b, c, and d with numbers. For example, you could graph y = 2x3+ 3x2– x + 2. Observe the graphed outcomes together (or independently if working alone). This is an investigation process to see what types of curves and lines you and your partner can produce with this equation.

Special Note:You may make any coefficient zero. This eliminates the variable. For example, if you wanted to make y = 3x2+ 2, a and c would be zero to cancel out the x3and the x terms.

  1. Discuss with your partner what you would like to see in a roller coaster. Graph different functions by changing a, b, c, and d to “design” your ideal roller coaster. Come up withat leastfour equations that when pieced together would make your ultimate roller coaster. Be sure to note what window sizes you’re using in your graphs. You may have to change the default size to better see each of the polynomials’ shapes.
  2. Use a drawing program (or draw by hand and scan) to recreate your roller coaster, and for each section, provide the equations you and your partner decided upon.
  3. Using complete sentences, describe the theme of your roller coaster (example: monsters), and give your instructor details as to what your roller coaster would look like, feel like, and what makes your roller coaster unique.

Whether you are doing this activity independently or collaboratively you will submit the following to your instructor as assignment “07.09 Polynomials Activity"

  1. Your answers to part 1. (8 points)
  2. Your rollercoaster with at least four pieces and four equations (one equation for each piece). (10 points)
  3. Your rollercoaster description (section D of part 2). (5 points)
  4. Your reflection — write a paragraph, of 3 or more sentences, as you reflect on this activity and your final product. You may use specificquestionsto guide your thoughts, if needed. (2 points)

If you choose to do the second half of this activity collaboratively you will also submit theCollaboration Componentas assignment “10.11 Collaboration Component.”

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