After seeing many students struggle with Graphing Quadratic Equations I decided to create this exploratory activity. This allows students to do the work themselves to understand how Graphing of Quadratics works by actually graphing each element and noting what has changed.
Introduce the topic to your class and maybe work through the source graph and the first activity. Then you can let them explore on their own and make their own observations. The key to this is to let them understand.
After completing, you can then introduce the vertex form of equation of a quadratic.