Transformations - Maths

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List a sequence of transformations which maps the graph of y=x^2 to the image with equation y=4*(2x-3)^2 + 1

  • Transformations - Maths -

    The general transformation equation is:
    g(x)=a*f(b(x-h))+k

    where
    h=horizontal translation (right if h>0)
    b=horizontal scaling (stretch if 1/b>1)
    a=vertical scaling (stretch if a>1)
    k= vertical translation (up if k>0)

    applied in the above order, i.e. according to the PEMDAS rule.

    So the transformed equation can be written as:
    let f(x)=x²
    then
    g(x)=4*(2x-3)² + 1
    =4*(2(x-3/2))² +1
    =4*f(2(x-3/2))+1

    Identify the values of h,b,a,k as given above and hence the sequence of transformations.

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