In regular cumulative voting your score total must add to some cap, say 100. This means in a [0,10] system you could give 10 candidates a 10 since 10*10 =100. Quadratic voting penalizes higher scores in an effort to get people to spread out their votes.
cost = score^2
This means in a [0,10] system you could give only 1 candidate a 10 since 10^2=100. However you can give four candidates a 5 since 5^2+5^2+5^2+5^2=100. This means that people have incentive not to bullet vote.
It has got a lot of fame and even been used in Colorado but I do not see how it is really any better. I am not really that well informed on the issues with cumulative voting. It does not really solve vote splitting so I never considered it viable.