I am a high school student studying calculus through YouTube lectures. The lecturer said that if replacing $(x,y)$ with $(-x,-y)$ makes no change, the curve is symmetric about origin. But if we replace $x$ with $-x$ and $y$ with $-y$ and we get no change then the curve is symmetric in all the 4 quadrants. I don't get what is the difference between both the conditions. Probably the condition for symmetricity in 4 quadrants means that if we have the curve as $f(x,y) = 0$ then $f(-x,y) = 0$ and $f(x,-y) = 0$ represent the same curve. Although I think that it will have symmetricity in 1st , 2nd and 4th quadrant only not in 3rd quadrant.
But for the condition of symmetricity about origin, I can't understand what does this mean at all.
(The above analysis is for any curve not just functions)