How to modify search input type?

I’d like to add two parameters to the HTML5 “input type=search” field in general-template.php (line 237). I know the -wrong- way to do this is to edit that line directly.

I -think- the right way to do it is to create my own searchform.php file in my theme, but I’m unclear what I should put there: do I need to recreate that entire section of the general-template.php file? Basically, all I want to do is change this …

<input type="search" class="search-field" ...>

… into this …

<input type="search" results="5" autosave="10" class="search-field" placeholder="'

Two parameters added to one line of the input field … so how do I pull that off?

thanks;
-rob.