Question 994033
f(x)=-x^2.  This opens up downward.  As x^2 gets larger, -x^2 gets larger negative, so the graph goes down with increasing positive or negative x.  
f(x)=x^2, here, when x is positive or negative x^2 is always positive, like the first case.  But there is no negative sign in front of the x^2, so the graph opens upward.

{{{graph(300,200,-10,10,-10,10,x^2, -x^2)}}}