Answer
No symmetry on x-axis, y-axis nor the origin.
See graph
The intercepts: $(0,0)$, $(2,0)$, $(0,0)$.
Work Step by Step
$$y=x^2-2x$$
Testing for x-symmetry:
$$y=(-x)^2-2(-x)$$ $$y=x^2+2x$$
Since the resulting equation is not the same as the original equation, there is no x-symmetry.
Testing for y-symmetry:
$$-y=x^2-2x$$ $$y=-x^2+2x$$
Since the resulting equation is not the same as the original equation, there is no y-symmetry.
Testing for origin-symmetry:
$$-y=(-x)^2-2(-x)$$ $$-y=x^2+2x$$ $$y=-x^2-2x$$
Since the resulting equation is not the same as the original equation, there is no origin-symmetry.
Rewriting the equation in vertex form:
$$y+(\frac{-2}{2})^2=x^2-2x+(\frac{-2}{2})^2$$
$$y+1=x^2-2x+1$$
$$y+1=(x-1)^2$$
Thus, the vertex is at $(1,-1)$.
At $y=0$:
$$0=x^2-2x$$
$$0=x(x-2)$$
$$x=0$$
$$x-2=0$$
$$x=2$$
Thus, the x-intercepts are $(0,0)$ and $(2,0)$.
The graph is as shown.
The intercepts are for x-intercepts $(0,0)$ and $(2,0)$, and for y-intercept $(0,0)$.
