
Funkytrip |

Quicken spell does not provoke an AoO and therefore no concentration check is needed if you are in melee range and want to cast a quicken spell.
Grapple states you need to make a concentration check to cast a spell.
I think that is where the confusion comes from. So yes, if you are grappled, you need to make a concentration check to cast a quickened spell.

Abraham spalding |

Quicken spell does not provoke an AoO and therefore no concentration check is needed if you are in melee range and want to cast a quicken spell.
Grapple states you need to make a concentration check to cast a spell.
I think that is where the confusion comes from. So yes, if you are grappled, you need to make a concentration check to cast a quickened spell.
Since this was well within the parameters that the OP posted I answered as I did -- which is to say exactly what you answered only worded differently and not quite as clearly since the situation was explained by the OP already.