Exploration: y = ax^2 + bx + c and y = a(x - h)^2 + k
Move the sliders to set the desired equation in the form
Move the yellow circle at the vertex so that the graphs have the same vertex.
The move the other yellow circle to stretch, shrink and/or reflect the graph until the two graphs coincide.
If the graphs are in the same location, the equations must be equivalent.
Use the equation of the purple curve to describe the location of both graphs.