Hi  ! Are you sure you're talking about 'Yahoo Search' and not search.yahoo.com  ? Cause if its's the latter : that's a browser hijacker. Assuming that's what you're dealing with :

Go to the 3-bar menu (or   'Tools') => Addons => Extensions and look for any unfamiliar or suspicious looking extensions, like e.g. :

SafeSearch Incognito SearchAssist Incognito SafeSearch net File Convertor and Search Addon

When you find any : remove them.

Do the same in Windows' Control Panel => Programs.

However :   most malware will be 'hiding' somewhere , so let's run malware scans :

Further information can be found in this article :
https://support.mozilla.org/en-US/kb/troubleshoot-firefox-issues-caused-malware?cache=no

Run most or all of the listed malware scanners.
They all work differently   -   what one program doesn't pick up, the other might.

Also see : https://malwaretips.com/blogs/yahoo-toolbar-removal/

Have tried numerous times to remove "yahoo search" from the default choices in the drop down Firefox/ Mozilla 56.0.1 search box to no avail! Have also tried to restore Firefox to its default state, removed unwanted programs in windows add/remove, disabled programs under services and did a yahoo search in the registry, to no avail! This should be my choice and only serves to make me more determined to avoid yahoo all together!

Like I said earlier : the culprit could be 'hiding' somewhere, hence the advice to run all those malware scans. Have you done that yet  ?

But : I'm still not sure whether you are talking about the legitimate search engine 'Yahoo Search' or the browser hijacker search.yahoo.com ..... (?)

Your first screenshot shows : Save Browsing Version 4 (temporary add-on), which is part of a Mozilla experiment. If you want to, you should be able to disable or remove it (it will be disabled at the end of the experiment anyway).

See for more information : https://support.mozilla.org/en-US/kb/shield

See for a hopefully happy end to this :

https://support.mozilla.org/en-US/questions/1180243

Eureka!

At least for me anyway.

The culprit is an add-on: "SafeSearch Incognito 4.66" somehow added itself to my add-ons. -There are preferences in the add-on for allowable search engines, and the possibility to turn on/off. Neither removed the default Yahoo even when searching in Google. - Only DISABLING the add-on ceased Yahoo from taking over.

F@#$ Off Yahoo!

Yahoo!

The first screenshot pouly5 attached shows a Search for Fire Fox extension that looks very suspicious (spelling Fire Fox that way).

cor-el said

The first screenshot pouly5 attached shows a Search for Fire Fox extension that looks very suspicious (spelling Fire Fox that way).

Hence I asked to remove any unfamiliar or suspicious looking extension ......