In Geogebra:

1. Make an interactive sketch that will let you show versions (stretch vertically, shift left right and up down) of 3 different parent functions by changing sliders. You should have hide-show checkboxes to go back and forth between the 3 functions. 

2. Make an interactive sketch that will let you show the constructions (intersections) that give you the incenter, circumcenter, orthocenter and centroid of a triangle, along with hide-show buttons for the lines and the centers.  Use your construction to discover and make a conjecture about a relationship between 3 of the 4 centers.