Does the equation y=x^2-x have y-axis, x-axis, or origin symmetry?
I let Wolfram graph it for you
http://www.wolframalpha.com/input/?i=plot+y%3Dx%5E2-x
As you can see, it is not symmetrical about any of the ones you mentioned.
e.g. (3,6) lies on your graph
If it were symmetrical about the y-axis, (-3,6) should be on the graph, it is NOT
If it were symmetrical about the x-axis, (3,-6) should be on the graph, it is NOTIf it were symmetrical about the origin, (-3,-6) should be on the graph, it is NOT
To determine the symmetry of a function, we can analyze its equation.
Let's start with the y-axis symmetry. To check for y-axis symmetry, we substitute -x for x in the equation and simplify it. If the resulting equation is the same as the original equation, then the function has y-axis symmetry.
Let's substitute -x for x in the equation y = x^2 - x:
y = (-x)^2 - (-x)
y = x^2 + x
As you can see, the resulting equation is not the same as the original equation (y = x^2 - x). Therefore, the function does not have y-axis symmetry.
Next, let's consider x-axis symmetry. To check for x-axis symmetry, we substitute -y for y in the equation and simplify it. If the resulting equation is the same as the original equation, then the function has x-axis symmetry.
Let's substitute -y for y in the equation y = x^2 - x:
-y = x^2 - x
Rearranging the equation, we get:
x^2 - x + y = 0
As you can observe, the resulting equation is not the same as the original equation. Therefore, the function does not have x-axis symmetry either.
Finally, let's examine origin symmetry. For a function to have origin symmetry, it needs to have both y-axis symmetry and x-axis symmetry. Since we have already determined that the given equation does not have y-axis or x-axis symmetry, we can conclude that it also does not have origin symmetry.
In summary, the equation y = x^2 - x does not have y-axis symmetry, x-axis symmetry, or origin symmetry.