So in one go, can a sorcerer cast quickened spell , witches bolt with advantage and fire bolt with advantage ? 

Quote from Born_Talent >>

So in one go, can a sorcerer cast quickened spell , witches bolt with advantage and fire bolt with advantage ? 

 Possibly, depending on the source of Advantage.

A Sorcerer  can cast Witch Bolt  as a Bonus Action with Metamagic: Quickened Spell and also cast Fire Bolt with an action.

Wether the attacks made as part of those spell have Advantage will depend on the game feature granting it.

One possible way could be through Level 1: Innate Sorcery, provided it was activated beforehand.

Quote from Born_Talent >>

So in one go, can a sorcerer cast quickened spell , witches bolt with advantage and fire bolt with advantage ? 

Normally you would not be able to do this because Witch Bolt is a leveled spell:

Quickened Spell

Cost: 2 Sorcery Points

When you cast a spell that has a casting time of an action, you can spend 2 Sorcery Points to change the casting time to a Bonus Action for this casting. You can’t modify a spell in this way if you’ve already cast a level 1+ spell on the current turn, nor can you cast a level 1+ spell on this turn after modifying a spell in this way.

Quote from up2ng >>

Quote from Born_Talent >>

So in one go, can a sorcerer cast quickened spell , witches bolt with advantage and fire bolt with advantage ? 

 

Normally you would not be able to do this because Witch Bolt is a leveled spell:

Quickened Spell

Cost: 2 Sorcery Points

When you cast a spell that has a casting time of an action, you can spend 2 Sorcery Points to change the casting time to a Bonus Action for this casting. You can’t modify a spell in this way if you’ve already cast a level 1+ spell on the current turn, nor can you cast a level 1+ spell on this turn after modifying a spell in this way.

 
Fire bolt is not a level 1+ spell, it is a cantrip.

So, yes, they can.

How do you figure?  That part that I italicized and underlined explicitly forbids you from doing so.  It pretty much has to be two Cantrips unless you have some other feature that overrides this restriction.

I will break it down step by step for you by checking the parameters. 

Witch Bolt as BA, then Fire Bolt as Action

I start my turn and intend to use the quicken spell metamagic for Witch Bolt first, then follow with my action for Fire Bolt.

First parameter: You can’t modify a spell in this way if you’ve already cast a level 1+ spell on the current turn

Check: have I already cast a level 1+ spell on this current turn?

Answer: No. I have not. I have not cast any spell this turn yet.

So, good to go so far. Witch Bolt is cast as a bonus action. On to Fire Bolt.

Next parameter: nor can you cast a level 1+ spell on this turn after modifying a spell in this way.

Check: Is Fire Bolt a level 1+ spell?

Answer: No, Fire Bolt is not a Level 1+ spell, it is a cantrip.

All parameters cleared. I can use my action to cast Fire Bolt.

-- 

Even if we reverse it, still all good.

Fire Bolt as Action then Witch Bolt as BA.

I start my turn and use my action to cast fire bolt. I then intend to use the quicken spell metamagic. 

First parameter: You can’t modify a spell in this way if you’ve already cast a level 1+ spell on the current turn

Check: have I already cast a level 1+ spell on this current turn?

Answer: No. I have not. I've only cast a cantrip which isn't a level 1+ spell.

So, good to go so far.

Next parameter: nor can you cast a level 1+ spell on this turn after modifying a spell in this way.

Check: have I modified a spell using Quicken Spell already this turn?

Answer: No, I have not modified any spells using Quicken Spell already this turn.

All parameters cleared. I can use my bonus action to quicken spell Witch Bolt.

The only thing you can't do is cast FB as the BA and WB as the action.

Quote from up2ng >>

How do you figure?  That part that I italicized and underlined explicitly forbids you from doing so.  It pretty much has to be two Cantrips unless you have some other feature that overrides this restriction.

 The  Metamagic: Quickened Spell put a restriction on what spell you can cast before or after the quickened spell, not the spell affected by the feature itself, which can be of any level spell that has a casting time of an action.