Question

How do you rearrange a quartic equation in the form of `ax^6 + bx^5+cx^4+dx^3+ex^2+fx+g` to vertex form (If possible)?

Answer 1

A few observations...

Explanation:

An equation is an expression that equates one thing to another, so would have to contain an equals sign somewhere.

The expression you have specified is a sextic (i.e. degree `6`) polynomial and not a quartic (i.e. degree `4`).

It can be understood to describe a function of `x`.

Its graph can have a total of `5` vertices, so it is not clear what you would mean by "vertex form" for a sextic.

An example would be the sextic Chebyshev polynomial of the first kind:

`T_6(x) = 32x^6-48x^4+18x^2-1`

graph{32x^6-48x^4+18x^2-1 [-2.5, 2.5, -1.25, 1.25]}