SOLUTION: For the given equation, list the intercepts and test for symmetry. y = x^3 - 216 I am having a hard time grasping this concept.

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Question 625792: For the given equation, list the intercepts and test for symmetry.
y = x^3 - 216
I am having a hard time grasping this concept.
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
For the given equation, list the intercepts and test for symmetry.
y = x^3 - 216
This equation is a difference of cubes
y+=+x%5E3+-+6%5E3
a%5E3-b%5E3=%28a-b%29%28a%5E2%2Bab%2Bb%5E2%29
y=%28x-6%29%28x%5E2%2B6x%2B36%29
x-intercepts
set y=0
0=%28x-6%29%28x%5E2%2B6x%2B36%29
x=6
two other roots are non-real %28b%5E2-4ac%29%3C0
y-intercept
set x=0
y=-6*36=-216
symmetry:none
see graph below:
+graph%28+300%2C+300%2C+-10%2C+10%2C+-1000%2C+1000%2Cx%5E3-6%5E3%29+