Creating Duplicate Objects in 3-Space

Here, we illustrate how the absolute value function can easily allow us to create duplicate surfaces in GeoGebra 3D Graphing Calculator. Here, we illustrate in GeoGebra Augmented Reality. How can we describe any symmetries (plane, rotational) seen here?

1 Paraboloid

1 Paraboloid

2 Paraboloids: Notice the |x| term in the equation below.

2 Paraboloids: Notice the |x| term in the equation below.

2 Paraboloids: Notice the |y| term in the equation below.

2 Paraboloids: Notice the |y| term in the equation below.

4 Paraboloids: Notice the |x| and |y| terms in the equation below.

4 Paraboloids: Notice the |x| and |y| terms in the equation below.

Quick (Silent) Demo