Do zupy potrzebuję marchewki, cebuli i jednej papryki.

Here do zupy means for the soup or to put in the soup.

In cooking Polish, do + genitive is very common for ingredients:

• do herbaty = for tea / in tea
• do sałatki = for a salad / in a salad
• do zupy = for soup / in the soup

It does not mean for the benefit of the soup. For that kind of for, Polish would use dla.

Because the preposition do requires the genitive case.

• dictionary form: zupa
• after do: do zupy

So zupy is simply the genitive singular form of zupa.

Potrzebuję is the 1st person singular present tense of potrzebować, so it means I need.

A few forms:

• potrzebuję = I need
• potrzebujesz = you need
• potrzebuje = he/she/it needs
• potrzebujemy = we need

So the sentence is literally structured as For the soup, I need...

That is a very good question. In Polish, many verbs do take the accusative, but potrzebować is one of the verbs that normally takes the genitive in standard Polish.

So:

• mam marchewkę = I have a carrot → accusative
• potrzebuję marchewki = I need a carrot / some carrot → genitive

That is why you get:

• marchewki
• cebuli
• papryki

instead of the nominative forms marchewka, cebula, papryka.

They are all genitive singular here:

• marchewka → marchewki
• cebula → cebuli
• papryka → papryki

So the sentence uses genitive both after do and after potrzebuję.

This is one reason Polish sentences can look unfamiliar to English speakers: the noun endings change a lot depending on grammar.

Because jedna must match the noun's case, gender, and number.

The noun papryki is:

• feminine
• singular
• genitive

So jedna changes to jednej:

• nominative: jedna papryka
• genitive: jednej papryki

Exactly the same thing happens with adjectives in Polish: they must agree with the noun they describe.

It usually means that the speaker is giving an exact number only for the pepper, but not necessarily for the carrot and onion.

So:

• marchewki, cebuli can mean a carrot and an onion or just some carrot and onion, depending on context
• jednej papryki clearly means one pepper

In recipe or shopping language, Polish often leaves one unstated unless the number matters.

If you wanted to make all three quantities equally explicit, you could say: Do zupy potrzebuję jednej marchewki, jednej cebuli i jednej papryki.

Polish does not have articles like a/an and the.

So Polish simply says:

• marchewki
• cebuli
• jednej papryki

and the exact English article depends on context:

• a carrot
• the carrot
• some carrot

Polish relies on context, word choice, and case endings instead of articles.

Yes. Polish word order is fairly flexible.

This sentence: Do zupy potrzebuję marchewki, cebuli i jednej papryki.

could also be: Potrzebuję do zupy marchewki, cebuli i jednej papryki.

Both are natural. Starting with Do zupy puts a little more emphasis on what this is for: as for the soup...

English depends much more on fixed word order than Polish does.

Here it means a pepper, most likely a bell pepper / sweet pepper.

Why? Because the sentence says jednej papryki = one pepper, so it is clearly talking about the vegetable.

The word papryka can also mean paprika as a spice, but context tells you which meaning is intended.