"How... dare you!? That's my BULMA!!!"
Upon being overcome by an extreme rage, the user powers up into their strongest form, however their power skyrockets even further than usual, temporarily blanking out their eyes. In this state, both his skin and body turns with a slight pink tone and blue bolts surround him.
After Beerus the Destroyer slapped Bulma and knocks her down, Vegeta becomes fully enraged and, after being transformed into a Super Saiyan 2, he undergoes a furious mutation. Vegeta powers up so much that he was able to briefly hold his own against Beerus. In the anime this power up is strong enough that Beerus says he had to use 10% of his power.
It is stated by Beerus that it has been a long time since he has used 10% of his full power, though this may not have been true, and may have been meant to anger Vegeta to further power him up; fighting him was even more fun than fighting Super Saiyan 3 Goku at King Kai's Planet. In the movie version, Roshi exclaims in amazement that Vegeta's power has finally surpassed that of Goku's.
After the battle Vegeta begins training himself in order to further power up and surpass Goku and Beerus, however he finds out from Whis that in order to do so he will need to learn how to control his ki from Whis, and goes back to Planet Beerus to train with him.
In the manga, during the "Future" Trunks Saga, Vegeta seems to be capable of utilizing the Quake of Fury power up at will, as Super Saiyan 2 Vegeta is able to hold an advantage over Super Saiyan Goku Black in battle.
Video game appearances
Quake of Fury is named in IC Carddass Dragon Ball, where it is used by Vegeta: Battle of Gods.