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How  convert a cubic equation in standard form ax^3+bx^2+cx+d to vertex form a(x-h)^3+k I need to know how to algebraically convert from standard form to vertex form not just say look of graph I am provided with with standard form and need to convert it to vertex form using algebra Thank You so much!

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We want to convert a cubic equation of the form `y=ax^3+bx^2+cx+d` into the form `y=a(x-h)^3+k` .

(1) Lets expand the vertex form:





(2) Equate the corresponding coefficients with the equation in standard form, thus:





(3) Then the required conversions are given by:




Example: Given `y=3x^3-18x^2+36x-20` we find:




So the vertex form is `y=3(x-2)^3+4` .

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