Here we go again!

You may use Yahoo as the default search engine in Firefox or set it as such.

• Please see Change your default search settings in Firefox

Yahoo does also actually produce searchbars for Firefox or did so. (I seem to recall they had problems keeping their software up to date)

If your search bar keeps changing to something odd you may have some form of malware adware or hijacker on your computer, if so please follow the instructions in

• Remove a toolbar that has taken over your Firefox search or home page
• Troubleshoot Firefox issues caused by malware

It may be worth you following a possibly related thread

• Why did Firefox screw up my Yahoo Toolbar?

https://downloads.yahoo.com/faqfirefoxtoolbar

On August 1, 2016 we will simplify the Firefox Yahoo Toolbar and upgrade your browser to the New Tab by Yahoo extension experience. This extension provides a static version of Yahoo Toolbar and customizes your new tab page with Flickr photos and quick access to your top sites. Please note, you will no longer be able to modify your toolbar layout.

Yahoo appears to have a simplified version of their toolbar extension at https://addons.mozilla.org/firefox/addon/yahoo-toolbar-and-new-tab/ and their https://toolbar.yahoo.com/ link leads to a more simple page.

There has not been any Firefox updates since the 47.0.1 to affect any extensions and next update will be Firefox 48.0 tomorrow.