This activity is to explore the difference between the standard equation and transformation equation for a parabola.
Use the sliders to align each parabola with the red points. By doing this the parabolas should be the same function.

Which equation is easier to place the parabola where you want it?

With the parabolas lined up exactly, they are should be the same function. See if you can use algebra to turn the transformation
equation you got in to the standard equation.

Were they the same? They should have been. Now a bit harder, convert the standard equation to the transformation equation.