So. What affects Varus and Xerath Q's?

This is a old question but I want to ask regardless. If you have a movement speed quint on or , would you be able to move faster while charging Q? Does the 'swiftness' mastery or affect them either? I know this has been asked before at some point or another, but honestly can't seem to find said answer at the moment, and I can't be bothered to look more. So why not make a bloody post about it.