Question

list the intercepts and test for symmetry y=x^3-512

Answer 1

You could start by factoring. We have here the difference of two perfect cubes. The equation for this is:
\[a^3 - b^3 = (a-b)(a^2 + ab +b^2)\] In this case, a=x and b=8. So:
\[x^3 - 512 = (x-8)(x^2 +8a +64)\]

Answer 2

so the intercepts are x=8 and y=-512

Answer 3

Yep, you can graph it to check those or make sure there are no other roots.

Answer 4

@vinnv226 question: can I do as follow to find out the roots?
x^3 -512 =0 --> x^3 = 512
x = cube root of 512 =8
by that way, I don't have any complex roots. Is it right?

Answer 5

Thats definitely a valid way to find the roots. But there are two complex roots. You know this because it's a third degree, so it must have three roots, and there is only one real root.

Answer 6

Got you, thanks for explanation.

Answer 7

I still have another question. Would you mind explain me?

Answer 8

If you're interested, the complex roots are
4(-1 - isqrt3)
4(-1 + isqrt3)

Answer 9

I 'll be back and make question later. I have a call. sorry

Answer 10

thank you. @vinnv226