Custom Search and Filter functionality VueJS

I was hoping I could get some feedback on something I'm working on. I'm building an application that is essentially a bunch of data tables. Part of my requirement is not to use any additional frameworks (vuetify) or any type of store (vuex).

Currently, my application is constructed as follows:

• API call upon creation of app
• That data get's passed into a component where I would like to do all my searching/filtering
• From there the next component is built specifically for Pagination
• Then to the component that builds the data tables.

My question is, since I have this top down approach, how do I build both the search and filter functionality to where I don't have to pass anything back up to the parent components?

I am using scoped slots to pass/inject data into child components. My first thought was that I would have a computed property that returns an array in the control component and then pass that down to the pagination component, which works, but how do I also use that same array if I want to be able to filter results and also search filtered and none filtered items? Essentially to be able to mock the functionality of some of the Vuetify tables.