Answer
For $y = x^2 - x + 8$, there is no graph that is symmetric neither to the $x$-axis, the $y$-axis nor the origin. There is none of them.
Work Step by Step
In $y = x^2 − x +8$,
a) To test for symmetry w.r.t the $x$-axis
replace $y$ with $−y$, we have
$(−y) = x^2 − x + 8$
$−y = x^2 − x + 8$
$y = -x^2 + x - 8$
which the result is not the same as the original equation, therefore, it is not symmetric with respect to the $x$-axis
b) To test for symmetry w.r.t the $y$-axis
replace $x$ with $−x$, we have
$y = (−x)^2 − (−x) + 8$
$y = x^2 + x + 8$
which the result is not the same as the original equation, therefore, it is not symmetric with respect to the $y$-axis
c) To test for symmetry w.r.t the origin
replace $x$ with $−x$ and $y$ with $−y$, we have
$(−y) = (−x)^2 − (−x) + 8$
$−y = x^2 + x + 8$
$y = -x^2 − x - 8$
which the result is not the same as the original equation, therefore, it is not symmetric with respect to the origin
