Conic+Sections+Project

=**Conic Sections Project ** =

You will be assigned the ID number for one of the following conic section equation pages. Your group has a unique set of systems, so it is important that you record the ID number in your planner.

For each system, you must complete the following:
 * Part I: Algebraic Representation**
 * 1) Rewrite (if needed) the equation in standard or vertex form.
 * 2) Name the conic section represented by the equation.
 * 3) If the conic is a


 * 1) **Parabola**, identify the following:


 *  Coordinates of the Vertex
 *  Minimum, Maximum, or Neither
 *  Function or not
 *  Domain & Range


 * 1) **Circle**, identify the following:


 *  Coordinates of the Center
 *  Radius
 *  Domain & Range


 * 1) **Ellipse**, identify the following:


 *  Coordinates of the Center
 *  Major Axis (horizontal or vertical)
 *  Length of the Major & Minor Axes
 *  Domain & Range


 * 1) <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif;">**Hyperbola**, identify the following:


 * <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif;"> The coordinates of each vertex.
 * <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif;"> The coordinates of the four vertices of the ‘drawing’ box.
 * <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif;"> Length of the Transverse Axis & length of the Conjugate Axis
 * <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif;"> Equations of the Asymptotes

You must graph each system using the following rules and guidelines.
 * Part II: Graphic Representation**
 * 1) Each system must be graphed on a separate sheet of graph paper.
 * 2) You must use two different colors for each system – one color for each graph.
 * 3) Each graph must be labeled by name and equation – (refer to #1 and #2 above).
 * 4) For each inequality, you must shade the intersection of the solution set (if any).
 * 5) __To the side (or above/below)__, include all components of #3 above that are relevant for each graphed equation.


 * Part III: Putting it All Together**
 * 1) You must create a title page containing:
 * 2) The title of your project
 * 3) Your name __and__ signed honor code
 * 4) A colored picture/illustration involving at least one conic section
 * 5) When finished, combine your pages in this order:
 * 6) Title Page
 * 7) Conic Section Problem Set (your original handout of 4 systems)
 * 8) The graphed inequalities in the order assigned on the original handout

Your project must have a theme (ex: summer days, fish bowls, and happy cats.) Your theme must be reflected on the title page, as well as on each graphed system.
 * Additional Requirement:**


 * Helpful Hints:**
 * 1) Remember to distinguish between solid and dashed lines.
 * 2) Remember to draw and label an appropriate coordinate plane.
 * 3) If you have difficulty determining the appropriate region to shade, remember to test a point.

**DUE: FRIDAY MAY 21, 2010**
 * Beginning of Class**


 * <span style="display: block; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; text-align: center;">10% Grade Reduction per Day Project is Late **