jQuery is not updating the forms action on hitting return

I'm trying to get the action attribute of my form to update on keypress. This is raising 2 issues:

1 - on hitting return, it only includes the first variable and the string needed to push the search, but misses the alterdLink var search query.

2 - the jQuery always misses of the final keystroke (The final keystroke can also be the first if you only type 1 character)

Here is my code:

    $('.search-box').on('keypress', function() {
        searchTerms = $(this).val()
        httpLoc = 'http://www.example.com/search'
        var alteredLink = searchTerms.replace(/\ /g, '+')
        if (alteredLink.trim() != '') {
            var fullLink = httpLoc + 'needed-string-for-search' + alteredLink //Misses this last var on hitting return
            console.log(fullLink)

            $('.search-form').each(function() { //The design forced the need fo several forms on the page...
                $(this).attr('action', fullLink)
            })
        }

    })

It will spit out the full link (minus 1 character in the alterdLink variable) to the console, but when you hit return it simply ignores this. THe code has the same outcoem whetherornot you use keydown, keyup or keypress. Any ideas?