Pre calc
posted by Anonymous on .
How do you test for symmetry in an equation? For example, y = x to the fifth power + x to the third power + x?

To test for symmetry, first you need to know what kind of symmetry you want to test for. Is it OverTheOrigin Symmetry, or OverTheXAxis Symmetry, or OverTheYAxis Symmetry?
First, you should rewrite your equation with new variables:
b = a^5 + a^3 + a
For ORIGIN SYMMETRY, substitute (a,b) for your x's and y's, respectively. Then solve your new equation to make it look like the equation above (so the b is not negative). Your solution should look like:
b = (a)^5 + (3a)^3 + (a)
b = (a^5) + (3a^3) + (a)
b = a^5 + 3a^3 + a
Because this equation is exactly the same with the equation above (b = a^5 + 3a^3 + a), it is symmetrical across the ORIGIN.
Now test it for Xaxis and Yaxis using these variable substitutes.
XAxis (a,b)
YAxis (a,b)
Make sure you double check your work! 
Oops! I'm sorry for the typo, it should be (a)^3 instead of (3a)^3. All the typos after that are the same. My mistake, I'm sorry.