The three transformations of a function are: standard form, vertex form and factored form. refer to the diagram for more info on what each variable within the equation does.
ie. y = x^2 - 6x + 11 is standard form.
y = (x-3)^2 + 2 is vertex form. These equations are equivalent but in different forms. Btw you can get factored for form standard form by factoring. hope this helps! :)