Chapter 12 Project

For your final Algebra 1 project of the year, you will be analyzing a parabola. All students will choose a different parabola to analyze, but will answer the same set of questions/problems about their choice. You should work individually on this project, but are welcome to seek advice from your classmates, from previous years' projects, or from Mrs. Shutters. There will be various due dates throughout the next few weeks to keep you on top of this big project. The final project is DUE FRIDAY, MAY 25, when you will give a brief (1-2 minute) presentation of your findings. You should create a new wiki page that will house your project data. If you cannot access the wiki for any reason, you are expected to complete the project in another way (such as using Word or by hand).

Follow the steps below to complete this project.
  1. Due Monday, April 30 - CHOOSE YOUR PARABOLA (1 sentence): You may choose any parabola that exists in a real-life situation. Your parabola cannot simply be something you draw on a graph in math class - that is not a real-life example! It must represent something, whether it be the shape of an existing item, like the McDonald's arches, or a curve that shows a pattern, such as the height of a projectile over time. We have mentioned several examples in class, and there are many in your textbook. Check out this video for even more examples:

  1. Due Tuesday, May 1 - CREATE YOUR WIKI PAGE AND DESCRIBE YOUR PARABOLA (1-2 detailed paragraphs): Find out as much as you can about your chosen parabola and write it on your wiki page. This may include, but is not limited to, the object's history, location, and architecture; people associated with inventing or building it; the science behind its formation, and any other interesting facts about it. Be sure to include any mathematical information you can find. At a minimum, this should include the height and width of your parabola If you can find it, also include: the equation of the parabola, the vertex/minimum/maximum, x- and y-intercepts, and dependent and independent variables. This section would be a great place to include some pictures, or even a video.

  2. Due Tuesday, May 8 - GIVE EQUATIONS FOR YOUR PARABOLA (3 equations and explanations/work): Using your research and/or graph, write an equation for your parabola. Include a description of how you got your first equation. Use what you learned in Chapter 12 to write your equation in 3 forms: standard form, vertex form, and factored form. You may have to complete the square to find the vertex form of the parabola - refer to Section 12-2 if you need assistance. Writing the equation in factored form may involve factoring - see Sections 12-4 and 12-5 for help with that. Include several sentences describing how you found each equation, and show all work. Check out the Help page for further assistance.

  3. Due Friday, May 11 - GRAPH YOUR PARABOLA (1 graph and 1-2 sentences): If your parabola is not already in graph form, you must graph it. You can use Grapher, desmos, another graphing program, or graph paper. Your graph should be very neat. Choose the window (frame limits) that shows the best view of the parabola. The vertex and intercepts (if applicable) should be visible on your graph. Mrs. Shutters will be happy to help with this part, especially if your parabola is an object that does not lend itself to graphing easily on paper (such as an arch). Check out her example project, or this Help page. Transfer an image of your graph to your wiki page.

  4. GIVE DETAILS ABOUT YOUR PARABOLA: This is the fun part - where you will discuss the nitty-gritty mathematics of your chosen parabola - and show everything you've learned in Chapter 12! Give information about each of the items below. Include detailed explanations, show all work, and include pictures, diagrams, or graphs if applicable. The more you have here, the better your grade will be.

    1. Due Wednesday, May 2 - VERTEX: What is the vertex of your parabola? How did you find it? How could you find it without looking at the graph? Is the vertex a minimum or a maximum? How do you know? What does the vertex signify for the situation (for example, it's the highest point a ball reaches or it's when the span of a bridge is closest to the road)? What is the equation for the axis of symmetry?

    2. Due Friday, May 11 - Y-INTERCEPT: What is the y-intercept of your parabola? How did you find it? How could you find it without looking at the graph? What does the y-intercept signify for the situation (for example, the starting point of a ball being thrown)?

    3. Due Tuesday, May 15 - DISCRIMINANT: Use your standard form equation to find the discriminant of your parabola. Tell whether or not your equation can be factored over the integers - see Section 12-6 for assistance. What else does the discriminant tell you about the parabola? (Hint - it has something to do with rational numbers!)

    4. Due Wednesday, May 16 - X-INTERCEPT(S): How many x-intercepts does your parabola have? How do you know? If it has one or two, what are they? How did you find them? How could you find them without looking at the graph? What do the x-intercepts signify for the situation (for example, the point at which a thrown ball hits the ground)? How is factoring your parabola's equation related to the x-intercepts?

    5. Due Wednesday, May 23 - PROBLEM/SOLUTION: Use the quadratic formula to find when your parabola is at a certain height. You may choose what height this is, or Mrs. Shutters will come up with a problem for you. Show all your work. How is the quadratic formula related to the work we have done in Chapter 12?

    6. Due Friday, May 25 - BONUS - FOCUS & DIRECTRIX: Look up what these terms mean and find their values for your parabola. You can look it up in an advanced mathematics textbook or online.

    7. Due Friday, May 25 - BONUS - CONIC SECTIONS: What do parabolas have to do with cones? Again, you might find this information in an advanced math textbook or online. The more details you have, the more points you get!

Check out Mrs. Shutters' example projectto see an idea of what your project could look like. You do not have to follow this format, as long as you follow all the instructions above. You also do not have to do the project on this wiki - you may do it on paper, Word, or another program. Again, just be sure to follow all the instructions above. In the table below, you can find how many points each part of the project is worth. Answering EVERY question and instruction listed above will earn you full credit in each area.

Points Possible
What is due?
Did I do it? (Check off)
Monday 4/30
Topic chosen, write topic sentence
Create wiki page

Tuesday 5/1
Description paragraph(s)

Wednesday 5/2
Vertex details

Tuesday 5/8
12 (4 for each eqn.)
Equations: vertex, standard, factored forms

Friday 5/11
Graph and description of graph

Friday 5/11
y-intercept details

Tuesday 5/15
Discriminant details

Wednesday 5/16
x-intercepts details

Wednesday 5/23
Problem written and solved

Friday 5/25
Bonus details if you like (worth up to 4 points each)

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