The degrees of freedom
The shape of the chi-squared curve is the cumulative density function or probability density function, depending of what you want, of a random variable #X# with a chi squared distribution with k degrees of freedom(#chi_(k)^2 #).The only factors that can interfere with the shape of those graphs are the parameters taken by the distribution, the chi-squared distribution only takes one parameter, that is, the degrees of freedom, so it is the only one that can interfere in its shape.
There is a twist thought , it is possible to have a Non-central chi-squared distribution , this is common in some areas of statistics and in that case you have an extra parameter
Here are some graphs of the central chi-squared distribtution:
If you having trouble understanding what the chi-squared means, maybe if you use the relation it has with other variables to enlighten you the relation it has with other variables to enlighten yourself