Question 420127
{{{y=-2x^2}}}
{{{graph(300,100,-10,10,-10,10,-2x^2)}}} The symmetry axis is y'y and the vertex is the origin O(0,0).
This result can be proved also because of the formula of this function f(x)={{{ax^2}}}, where a=-2...
(i)This x squared gives f(x)=f(-x) ,that is for every x the symmetric points 
(x,f(x)) and (-x,f(-x)) belong to the graph.[these points are (x,f(x),(-x,f(x))and we know the are y'y-symmetric as any two points (a,b) and (-a,b) are.]
(ii)a=-2 that is a<0 
so {{{ax^2<=0}}} ,that is the maximum value of f(x)=0 occurs when x=0,and (x,y)=(0,0) is the vertex of the parabola.