SOLUTION: Find x intercept, y intercept, determine symmetry for equation x^4 -25x^2 = y^3

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Question 751484: Find x intercept, y intercept, determine symmetry for equation x^4 -25x^2 = y^3
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find x intercept, y intercept, determine symmetry for equation
x^4 -25x^2 = y^3
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x-intercepts:
Let y = 0
Then (x^2-5x)(x^2+5x) = 0
x(x-5)x(x+5) = 0
x = 0 or x = 5 or x = -5
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y-intercepts:
Let x = 0
y^3 = 0
y = 0
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Symmetry:
f(x) = cbrt[x^4-25x^2]
f(-x) = cbrt[x^4-25x^2]
-f(-x) = -cbrt(x^4-25x^2)
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Since f(x) = f(-x) you have y-axis symmetry.
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cheers,
Stan H.