nominal adjective or noun?

In the following sentences is "bad" a noun or a nominal adjective: "You have to take the bad with the good" and "Things went from bad to worse"

These are all adjectives, not nouns.

In sentences such as:

1. The worst is yet to come.

The subject NP has a determiner the and a fused-modifier head, worst, which is a superlative adjective. It is not a noun. It does not “become” a noun. It remains an adjective.

Consider how different it is from this sentence with an actual noun in the same slot:

2. The surprise is yet to come.

How can you tell that (1) has an adjective but (2) has a noun? You can apply an intensifier like truly to adjectives but not to nouns. This is grammatical:

3. The truly worst is yet to come.

But this is not:

4. *The truly surprise is yet to come.

So even though worst is still an adjective, it is the head of the subject NP because it’s a fused-modifier head.

Not all NPs need contain nouns. Rather, they are syntactic constituents that serve in the grammatical role of subject, object, and so forth. That doesn’t mean they have to have a noun in them. Many do not. This is one such.

The bad is the direct object of your verb take. So is the good. There is no noun there, just an NP containing an adjective as a fused-modifier head. You can tell they’re adjectives because you can apply intensifying adverbs like truly to them, which can’t be done to nouns.