What happens when $y=4x^2$ and $y=8x^2$ is multiplied? When parabolicfunctions mentioned above are added, we get a new function with equation $y=12x^2$. But when we multiply these two function what is the result? 
Please explain by drawing graphs.
 A: 
But when we multiply these two function what is the result? 

Then you no longer get a parabola, but a similar graph in the sense that the properties of all the graphs of the form $y=ax^{2n}$ (even powers) are similar (see remark below). The function would be:
$$y = 4x^2 \cdot 8x^2 =4\cdot 8\;x^{2+2} = 32x^4$$

Please explain by drawing graphs.

Take a look.

To get an idea of how the (even) exponent influences the graph, take a look at the graphs of the functions $x^2,x^4,x^6$ (ignoring coefficients, they only scale) and note that the higher the exponent, the flatter the graph for $x \in [-1,1]$ and the steeper outside of that interval.
A: If you want to generate a graph of (pretty much any) function you can think of, try this calculator out. I put the functions you were talking about in for you already.
I think the stumbling point for you here is that "paraboloids" are just setting $y$ equal to expressions in terms of a variable $x$, and that anything you can do to a number can be done to these expressions with equal validity.
