What value in Vertex Form moves the graph up?

So far, so good. Now you cite the transitive property of congruence, saying objects congruent to congruent objects are congruent.

(IMO, another step might be needed. You have 2 ≅ 1 ≅ 7 ≅ 5, but you may have to show 1 ≅ 5 or 2 ≅ 7 before you can jump to 2 ≅ 5. The transitive property is usually written in terms of only one intermediate: a ≅ b ≅ c ⇒ a ≅ c.)