Can a multiclassed sorcerer/warlock use Quickened Spell to cast Green-Flame Blade and then use the Thirsting Blade feature to get 3 attacks on a turn?

Question

Can a multiclassed sorcerer-warlock use the Quickened Spell metamagic to cast a spell like green-flame blade as a bonus action, and then use the Thirsting Blade warlock feature to make 2 more attacks on the same turn?

Answer 1

This works but it requires your bonus action and action

The Thirsting Blade Invocation states:

You can attack with your pact weapon twice, instead of once, whenever you take the Attack action on your turn.

The Thirsting Blade Invocation requires you to take the Attack action. Simply making an attack does not count as doing this, as discussed in the following questions: "Can you combo attacks with the Booming Blade cantrip?" and "What does upper-case-A-Attack action vs. lower-case-a-attack mean?".

When you cast the green-flame blade spell (even if you do not quicken it) you are not taking the Attack action, instead you are taking the Cast a Spell action. What you can do is the following:

1. Cast Quickened green-flame blade (attacking a creature).
2. Take the Attack action, allowing you to attack twice with your pact weapon.

Another option is the following:

1. Take the Attack action, allowing you to attack twice with your pact weapon.
2. Cast Quickened green-flame blade (attacking a creature).

You would make three attacks total using up both your action and bonus action (and some sorcery points). Note that you can move between the two attacks you make with the Attack action, this is because the section on "Moving Between Attacks" states:

If you take an action that includes more than one weapon attack, you can break up your movement even further by moving between those attacks. For example, a fighter who can make two attacks with the Extra Attack feature and who has a speed of 25 feet could move 10 feet, make an attack, move 15 feet, and then attack again.

The third option of having the Quickened green-flame blade occur in-between the attacks of your Attack action is more up to your GM than anything else, and is discussed in the question "Can you break up your Attack action for a bonus action?"