Quadric Functions Challenge

1. Create an image using at least four of the quadric functions:

Ellipsoid (includes sphere)
Hyperboloid of on sheet
Hyperboloid of 2 sheets
Elliptic paraboloid or cone
Hyperbolic paraboloid.

You may use any type of surface more than once, but use at least 4 types.

2. At least two of these surfaces must be translated and at least two must be rotated. (You may do both to one surface.)

Write your equations in standard form. For example: (x-2)^2 /9 + (y+2)^2 /4 + (z-8)^2 = 1

Tips on using the grapher at: (Use the first one - multitype grapher.)
http://www.butlercc.edu/mathematics/math_courses/ma253/MA253_resource_page.cfm

This may take a few seconds to load. It needs "Java" which most browsers already have.

For quadric surfaces - Choose Graph to Add-> pick Implicit Surface; keep picking this to add surfaces
“Zoom fit” is an autoscale feature; under the bounds tab you may want to check use clip bounds
Note that there are two sets of bounds - the bounds on how far you plot (under the Graph tab), and the bounds for the whole graph (under the Bounds tab)
Use * for multiply, / for divide, and ^ for exponent
To increase the smoothness of your surface use discr; increase slowly or you’ll have to wait
Write down your surface equations and bounds as you go in case of a glitch (e.g. crash)
A good way to save your work is to have notepad or a word processor open so you can copy over the equations as you type.
You can bring them in from your document if you need to start over. Remember to type in your bounds also.
If nothing plots, either you have a syntax error such as leaving out *, or your bounds are too narrow
To see how to save your picture and email it see below

Quincy Q. Quadric:

	Equations and Variable Ranges Overall bounds: x [-5,5] y [-5,10] z [-5,15]
	ellipsoid: x^2 + (y-5)^2/9 + (z-6)^2 = 1 Bounds x [-5,5], y [-5,8], z [0,7]
	hyperboloid of one sheet: -x^2 + (y-2.5)^2/(1/9) + (z-3)^2/(1/9) = 1 Bounds x [-3,3], y [-5,5], z [-5,5]
	elliptic paraboloid: z = 14 - (x^2+y^2) Bounds x [-3,3], y [-5,5], z [12,14]
	ellipsoid: (x-1)^2 + (y-2)^2 + (z-8)^2 = 1 Bounds x [-3,3], y [-5,5], z [-5,5]
	ellipsoid: (x+1)^2 + (y-2)^2 + (z-8)^2 = 1 Bounds x [-3,3], y [-5,5], z [-5,9]
	hyperboloid of two sheets: x^2 - y^2/(1/9) - (z-8)^2/(1/9) = 1 Bounds x [-3,3], y [-5,5], z [-5,11]
	ellipsoid: x^2 + y^2 + (z-6)^2/9 = 4 Bounds x [-3,3], y [-5,5], z [-5,12]
	hyperbolic paraboloid: z = x^2/4 - y^2 Bounds x [-3,3], y [-5,5], z [-5,5]

Steps to create an image file to attach to an email:

1. Use the math tool to create the graphic.

sphere image

2. Hit the "Print Screen" key. This is often labeled Prt Scn and you may have to hold down the Fn key on a laptop.
This stores a screenshot of the whole screen.

print screen key

3. Start Paint or another graphics program: Start | All Programs | Accessories | Paint

paint program

4. Do Edit | Paste to put your screenshot into Paint.

edit paste menu

5. Crop the picture by using the rectangle button to select an area and then Edit | Cut .

Do File | New (don't save changes), then Edit | Paste
Now you have your graphic image.

You may want to type in some information over your graphic using the text key.

6. Now File | Save As Give it a name and remember to note where you save it.
Make sure you "Save as type" JPEG! Otherwise it will be a huge file!

7. Email to me as an attachment.