How does the Quickened Spell metamagic interact with the Haste Spell?

Question

Action + Bonus Action + Special Haste Action?

If an action + movement is taken, and a quickened spell is taken as a bonus action, and the quicken spell is Haste. This grants an action under these specific rules: Attack (one weapon attack only), Dash, Disengage, Hide, or Use an Object action.

I believe that would be two spells and a melee attack, or one of the other Haste actions? Is there a caveat with the bonus action? I heard you can only cast a cantrip on the bonus action, but haven't found it yet in the PHB.

Quicken: When you cast a spell that has a casting time of 1 action, you can spend 2 sorcery points to change the casting time to 1 bonus action for this casting.

Haste: Choose a willing creature that you can see within range. Until the spell ends, the target’s speed is doubled, it gains a +2 bonus to AC, it has an advantage on Dexterity saving throws, and it gains an additional action on each of its turns. That action can be used only to take the Attack (one weapon attack only), Dash, Disengage, Hide, or Use an Object action. When the spell ends, the target can’t move or take action until after its next turn, as a wave of lethargy sweeps over it.

Answer 1

Haste is a Red Herring; you're limited by casting a spell as a bonus action

In the PHB page 202 under Bonus Action, it states:

You can't cast another spell during the same turn, except for a cantrip with a casting time of 1 action.

Given that, we can work with how we can cast spells.

If, on your turn, you quickened cast Haste, that leaves you with your Action, as well as the limited action granted to you by the Haste spell itself.

You can use your regular Action for anything you normally could, unless you want to cast a spell, in which case you fall back to the rules provided with casting a spell as a bonus action (i.e. - it must be a cantrip with a casting time of 1 action).

Then you can use the Haste action to "take the Attack (one weapon attack only), Dash, Disengage, Hide, or Use an Object action".