Ocr C1 Graph Drawing

Hi.
Please could someone explain to me why for question 4(ii) it is not suitable to rearrange the equation to draw a graph with a +x^3 instead.
Are they not equivalent?
https://a9497d7f220e174d38d014b2b1d86a68bedc42a8.googledrive.com/host/0B1ZiqBksUHNYNExoNEtSS1ViN2c/for-OCR/Solomon%20G%20QP%20-%20C1%20OCR.pdf
Thanks.

No, they are only equivalent if you had it = 0.

i.e: roots are invariant under reflection. If you were to re-arrange the equation to get +x^3 you've reflected the graph in the x-axis, which is a totally different graph.

However, if you had 4x - 3x^2 + x^3 = 0 - then you can re-arrange it however you like because the roots remain invariant under reflection.

Thanks!,
what if i had 4x - 3x^2 + x^3 = 7 etc.
can i rearrange it then?

Yes, then you can re-arrange it because it's the same thing as 4x - 3x^2 + x^3 - 7 = 0 (i.e: still a root of some equation and hence still invariant).

You`d make a good maths teacher.
Thanks again