Will I lose the mark

It depends, what was the question?

Per above, it really depends on context. That said, I would never leave an expression alone in a page without an equal sign, as you could be doing f(x)="blah" (in which you want to investigate properties of the quadratic), or "blah"=0 (in which you want to solve the quadratic). Not writing either means your intention is unclear.

Talking from a "writing good maths" perspective, you should think of every line you write as a sentence.
"x^+4x+4" is not a sentence - it's missing a verb (in most cases it's the equal sign).

I find it surprising how common this is. I see this mistake from students all the time, across all ability levels.

I don't think maths teachers (that I know of) ever teach about writing maths properly. Such a shame...

Some do.

I was very disappointed when GCSE got rid of the marks for "quality of written communication" in the new spec. If it's examinable then it will be pushed harder in schools.

What I find interesting is that the students I see missing the "=0" when solving quadratics never make a similar mistake in any other algebra working. I think it might be because a lot of students see quadratic factorising and writing down solutions as just a method that they regurgitate without really understanding it properly.