Isabela's Ongoing Search is an Act 2 companion quest for Isabela in Dragon Age II, where she asks for help with another lead on the Relic.
Acquisition
Received with other companion quests as Hawke begins Act 2.
Walkthrough
Go to The Hanged Man and speak with Isabela.
First response:
Diplomatic: 
Isabela: rivalry (+5)
Humorous: 
Isabela: friendship (+5)
Aggressive: Isabela: friendship (+5)
Second response:
Diplomatic: Isabela: friendship (+10)
Flirt: Isabela: friendship (+25)
Humorous: Isabela: friendship (+15)
(tested on Xbox patch 1.04: no approval change for the humorous option. Using aggressive response results in no approval gain/loss. Diplomatic response now yields +15 Friendshipl).
Result
The max Friendship you can get is Isabela: friendship (+25)
The max Rivalry you can get is
Isabela: rivalry (+5). If you chose to flirt with her, you begin a romance with Isabela.