Someone just asked this same thing, try doing the search for topics and find answers that way too.
A murphy bed does not fold, if it folds then it is a folding bed.
It looks like your model is a murphy bed, that just folds flat up to the wall (mattress does not bend). The only struggle would be that you have to move the sofa backrest before folding the bed down. Folding down a bed is so simple and takes no time. Getting it out of the way is great. Your mattress will be fine standing vertical. If it folds then of course the folded part will get wear of some sort.
I had one that folded to the side, and it took one second to fold up, and 3/4 of one second to fold down at night. Time sacrificed was well worth it.