Of course you can build a search and pass parameters:
https://drive.google.com/file/d/0B1_PFw--3o74YjVreHNBOWU2aEE/view
You have to pass the "filters" in the url or query string. HTTP and HTML 101.
Also see
https://laracasts.com/discuss/channels/laravel/filter-and-pagination-1
and
https://laracasts.com/discuss/channels/laravel/laravel-5-query-builder-search-filter
On the example here https://laracasts.com/discuss/channels/laravel/filter-and-pagination-1
If NOT using query string, you "build" parameters in your uri and pass as route parameters.
Jeffrey has video lessons, and there's documentation.
This "basic" passing parameters and query string usage should be mastered before delving deep into laravel.
Since crud is the main usage of a php framework, or a web database application.
Building search filters has also been discussed in depth.
If not paginating, just one post will work. If pagination the first search is "posted", thereafter "get" is used.
If you only knew how many times a search, query string, passing parameters, etc has been discussed here in the past.
I even posted a guide to help people find prior good laravel answers: But I will put it here again:
Go to google, in search type:
site:laracasts.com your search
//as example
site:laracasts.com build search filter
// or
site:laracasts.com dependent dropdown
Don't just search what I gave as example, put in some of your own search terms.
I can tell you that car drop downs for a car search has been discussed before.