Chapter 10 Project: Designing a Conic Face



Chapter 10 Project: Designing a Conic Face

For this project you will be designing a face using only the conic sections that we have studied (Circles, Parabolas, Ellipses, and Hyperbolas). Your finished product should be done on GRAPH PAPER ONLY.

Part 1: Drawing the face

Draw a face on graph paper using the shapes mentioned above. Be creative! The requirements are listed below.

Your face must include AT LEAST the following:

• 2 circles

• 2 parabolas

• 2 ellipses

• 1 hyperbola

You must have AT LEAST a total of 10 conic sections in your drawing. 10 points will be taken off of your final grade for each one missing.

When drawing your face, be sure to draw in shapes that will create nice equations. For example, do not choose draw a hyperbola with a center at (-1.74, 3, 48). Instead, choose a hyperbola with center at (-2, 3).

You will be graded on effort and creativity. Keep in mind that the above requirements are minimums, and a face that goes above and beyond the minimum will most likely be graded higher than the most basic face.

Part II: Creating equations for the face.

Every shape on your paper must be numbered. On a separate piece of paper, you will create equations for the shapes that you have drawn. Your work should be neat and easy to follow. It should also be numbered to match your drawing. For example, if #1 on your drawing is a circle, then #1 on your sheet of work should be the equation that matches that circle.

These equations will make up the bulk of your grade. Be sure to double check your work for errors, as these will be graded on correctness.

An example of the work you should have is shown on the following pages.

For each shape, you must find the important info listed below. It does NOT need to be listed on your graph.

Hyperbola: Parabola: Ellipse Circle

Center Vertex Center Center

Vertices Focus Vertices Radius

Asymptotes Directrix Foci

Foci

Part III: Limiting the Domain and Range

As you know, all parabolas and hyperbolas continue on infinitely. This could make for a very strange looking face! In order to have our face stop where we want it to, you must limit the domain and range for these conics.

To limit the domain and range, look at the example work pages, which we will review in class before you begin your work.

Part IV: Presentation

Because this project is a test grade, it should be approached seriously and with obvious time and effort put in. The finished project that you hand in will have a considerable effect on your grade. If you turn in a crumpled piece of paper with scribble marks, don’t expect a high grade! Your final product must be on graph paper, should be colored in, should NOT have things crossed off or scribbled out, and would preferably be mounted on poster-board. Your project should be large enough for an entire class to see when it is posted on the wall.

Your project will be graded according to the following rubric:

Creativity: 15 points

• Does the project only meet the minimum requirements?

• Does the project use conic sections in way that differs from our class example?

• Is the project unique? (Do not copy another’s project. Trust me, I’ll notice)

• Is the project colored?

Equations: 50 points – 5 points each

• Does each shape have a corresponding equation?

• Is all the required information there?

• Are the equations correct?

o If an equation is incorrect, a point will be taken off for each mistake. For example, if you mix up the signs for the center of an ellipse and find the value of a incorrectly, you will only receive 3 out of 5 points for that equation.

Limiting Domain and Range: 15 points

• Are the correct conic sections limited?

• Are they limited correctly?

Presentation: 20 points

• Is the project neat?

• Is the project well-organized?

• Is the finished product well-displayed?

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