Google Classroom
GeoGebraClasse GeoGebra
GeoGebra

Exploring 3D surfaces

Auteur :clarke713
We are going to use the skills we learned when we working the 3x3 equations in geogebra to explore some surfaces. You may work with a partner and of course ask me questions as well. You will probably need some paper for a couple of questions. Remember that it is very helpful to use the move tool (arrow) especially after making changes to see what is going on from different prospectives.

Think for a minute about what you think the equation might look like on the 3D plane. Type what you imagine in the answer box.

Graph the equation in the input line in the graphing window below.

Use the arrow tool and move the graph around and take a look. What are you noticing and wondering about. Make notes in the answer box about what is similar or different than you imagined and anything you are wondering about.

Based on what you have done so far, what do you think the equation will look like in the 3D plane, put your description in the answer box. After you have entered your prediction graph the equation below in the next window. How close were you on this one?

If in the equation above find the the point on the surface and enter it in the second input line to see if you are correct. Remember it is 3D so it is an ordered triple. Type any thoughts or questions in the answer box below along with your point.

On the next graph we are going to enter both equations that we have used. So enter and in the first two input lines in either order. Change at least one surface to a different color. Move it around with the arrow tool and think about what you looking at for a minute or two.

If find the point of intersection of the two surfaces using skills you have from solving systems of equations and mathematics in general. Enter your solution below and then on the graph in the input line and see if you are correct, if not try again to figure out what went wrong.

What do you expect the graph to look like if we change the second equation to , enter your thoughts then enter the equation in the input line and see if you were correct.

If and , find a value of z that will create the an ordered triple that is on the surface. Enter you answer below then in the graph above and check your work.

(2,2,1) is also on the surface. Plot this point and then connect the two points with the segment tool.

Try to determine the distance between the two points by using something you know about distance on the Cartesian Plane. Enter your answer below.

Now use the line measuring tool and see if your answer agrees with the one you calculated. Enter your thoughts below.

System of 3x3 challenge. Given the solution find a possible set of three equations in three variables that has this solution. After you think you have them graph them and see if you are correct, since there are infinite solutions you know the intersection of the three should be a line.
Try to write an equation that projects a three dimensional ellipse that is centered at the origin. Then try to move the center to (2,-3,4)

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