Explanation for behaviour of graph of $y=x^2e^{-x^2}$ (Maxwell-Boltzmann distribution) Consider the function
$$y=x^2e^{-x^2}$$
The graph initially behaves as a parabola then in later part exponential part of it dominates; i.e., the graph looks exponential after maximum of the curve.
Actually this graph is related to Maxwell Boltzmann distribution graph. Please help me so that I can easily remember the property of this graph.

You actually gave the mathematical explanation.  The graph is below.  Over the range $[-1,1]$ the exponential doesn't change that much-it is $1$ at the center and $\frac 1e \approx 0.3679$ at the ends.  That is less than a factor $3$.  The parabola is $0$ at the middle and $1$ at the ends, an infinite ratio.  It dominates the product over this interval.  As you get outside that interval, the exponential dominates.  From $1$ to $3$ the parabola rises by a factor $9$, but the exponential drops by a factor $2980$, so it dominates.

