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    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://a9497d7f220e174d38d014b2b1d8...20C1%20OCR.pdf
    Thanks.
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    (Original post by SamuelN98)
    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://a9497d7f220e174d38d014b2b1d8...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.
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    (Original post by Zacken)
    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?
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    (Original post by SamuelN98)
    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).
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    (Original post by Zacken)
    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
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    (Original post by SamuelN98)
    You`d make a good maths teacher.
    Thanks again
    Thank you! That's a compliment if I ever saw one. :lol:
    Good luck with your exams!
 
 
 
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