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

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


   

Question 138691: Is the equation y%5E4%2By%5E2-7=3x%2B5x%5E2 symmetric about the x-axis?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Remember, if f%28x%29=-f%28x%29, 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.

y%5E4%2By%5E2-7=3x%2B5x%5E2 Start with the given equation


%28-y%29%5E4%2B%28-y%29%5E2-7=3x%2B5x%5E2 Replace each "y" with negative y


y%5E4%2By%5E2-7-7=3x%2B5x%5E2 Raise -y to the fourth power to get y%5E4. Raise -y to the second power to get y%5E2

Since the first equation y%5E4%2By%5E2-7=3x%2B5x%5E2 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