What is the meaning of adjectives ending in 〜く?

Question

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?

Answer 1

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.

Answer 2

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

Or these examples might help from Reddit discussion:

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