Answer
None.
Work Step by Step
Step 1. To test symmetry with respect to the x-axis, replace $y$ with $-y$, we have $-y=x^2-x+8$ or $y=-x^2+x-8$ which is different from the original, thus it is not symmetric with respect to the x-axis.
Step 2. To test symmetry with respect to the y-axis, replace $x$ with $-x$, we have $y=(-x)^2-(-x)+8$ or $y=x^2+x+8$ which is different from the original, thus it is not symmetric with respect to the y-axis.
Step 3. To test symmetry with respect to the origin, replace $x,y$ with $-x,-y$, we have $-y=(-x)^2-(-x)+8$ or $y=-x^2-x-8$ which is different from the original, thus it is not symmetric with respect to the origin.