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!
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` .