Question 91772
Answers:

1) notice that the exponent is -2, an even number so it is symmetric about y axis

see graph below:

{{{graph(200,200, -3,3, -1,10, x^-2)}}}

2)the vertex is infinity, when x approaches 0, {{{x^(-2)}}} approaches infinity

3)If you move the graph of {{{y = x^2}}} one unit to downwards, you get the  
graph of {{{y = x^2 -1}}}

see graph below

{{{ y = x^2}}} -- red; {{{y = x^2-1}}} -- green

{{{graph( 200,200, -3,3, -2,10, x^2,x^2-1) }}}

4) I am not sure if your question is a valid one or not. Basically these two have nothing to do with each other. See graph below.

{{{graph(200,200, -3,3, -10,30, x^2,x^-6+5)}}}