SOLUTION: Is the equation {{{y^4+y^2-7=3x+5x^2}}} symmetric about the x-axis?

Question 138691: Is the equation symmetric about the x-axis?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Remember, if , then the equation is symmetric about the x-axis. So in this case, we only need to replace y with negative y and see if the equations are equivalent.

Start with the given equation

Replace each "y" with negative y

Raise -y to the fourth power to get . Raise -y to the second power to get

Since the first equation is equivalent to the last equation, this shows that graph is symmetric about the x-axis

For visual proof, here's the graph:

From the graph, we can see that equation is symmetric about the x-axis
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