Anatomy of a Persuasive Argument

ethos: To get what you want from your parents they have to know you are responsible enough or they'll deny you right on the spot. For instance asking for a cellphone. Handling a phone takes much responsibility since it something so expensive and can be easily lost or maybe even broken.

pathos: Getting something you want usually has many reason behind it whether it be wanting to fit in with society and having the latest gadgets. Back to the example of asking for a phone, having a new phone may be your way of not feeling left in society. So you probably persuade your parents that just want to feel included instead of left out. It's quite sad how society has judged people based on the things they have.

logos: to appeal logically to your parents, you need to state the reasons why you need the thing you are asking for. If it is a phone you are asking for, tell them it's a way to contact in case of emergencies or something urgent that you need a way to contact.  

kairos: Today in society, having the latest gadget is somewhat a trend. For example, airpods. When it first came out, it wasn't really liked by many. However, now you can't even go through a day without seeing someone having it plugged into their ears.