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I understand that the following words are adjectives:

> 早{はや}い early/fast
>
> 近{ちか}い close/near
>
> すごい awesome/great

However I’m unsure how to use the forms ending in 〜く such as:

> 早{はや}く
>
> 近{ちか}く
>
> すごく

Do these have a different meaning or usage? An explanation of the differences
in grammatical role (if there is one) and examples of the different uses of
one of these would be helpful to understand the distinction. Examples of
polite (〜ます) and conversational sentences would help if usage is different
between them.

Are these special cases? If so, are there any other commonly used examples?

Can this form be used for any adjectives ending in 〜い? If so, is there an
equivalent form for adjectives ending in 〜な?
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usage adjectives adverbs i-adjectives adverbial
What is the meaning of adjectives ending in 〜く?
For 近い and 近く, try to think of 近い as an adjective meaning "close", "nearby",
and 近く as an adverb (?) meaning "in the vicinity".

> 駅{えき}が近{ちか}いです。  
>  The station is nearby.
>
> 駅{えき}は、スーパーの近{ちか}くです。  
>  (lit)The station is in the vicinity of the supermarket = The station is
> near the supermarket.

[Source](https://www.japanesepod101.com/forum/viewtopic.php?t=4244)

Or these examples might help from [Reddit
discussion](https://www.reddit.com/r/LearnJapanese/comments/20ipcl/%E8%BF%91%E3%81%8F%E3%81%AEx_vs_%E8%BF%91%E3%81%84x/):

近くのコンビニに行こう -- Let's go to the nearby convenience store.

近いコンビニに行こう -- Let's go to the close convenience store.

**Update** :

Really nice article about [すごく vs すごい](http://www.japaneseammo.com/you-may-be-
using-sugoi-and-kakkoii-wrong/)
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It is simply the adverbal forms of adjectives.

For い-adjectives, the ending is changed to く:

> 早｛はや｝い 早｛はや｝く
>
> 強｛つよ｝い 強｛つよ｝く
>
> 楽｛たの｝しい 楽｛たの｝しく
>
> すごい すごく

For な-adjectives, a に is added to the end:

> きれい きれいに
>
> 本当｛ほんとう｝ 本当｛ほんとう｝に
>
> にぎやか にぎやかに

The only exception I can think of at the top of my head is いい -> よく (comes
from よい)

Some examples:

> ご飯｛はん｝を早く食｛た｝べなさい！ = Eat (finish) your food quickly!
>
> 部屋｛へや｝をきれいにしました。 = I made my room clean.
>
> ご飯はいつもすごく美味｛おい｝しく作｛つく｝ってくれます。 = She always makes very delicious food.
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