Converting a vertex form to a standard form is considerably easier than converting from standard form to vertex form. Taking an equation in the vertex form (eq. 1) we can follow the process to convert to a standard form.

Eq. 1: \(y=(x+3.5)^2-0.25\)

First of all, the vertex form contains a square of a bracketed term. This is equivalent to the same bracket appearing twice (eq. 2).

Eq. 2: \(y=(x+3.5)(x+3.5)-0.25\)

This can be expanded using the same FOIL approach used to convert a factored form to a standard form to give us a collection of terms from multiplying out the contents of the brackets (eq. 3).

Eq. 3: \(y=x^2+3.5x+3.5x+12.25-0.25\)

Like terms can then be combined to give the expression in the standard form (eq. 4).

Eq. 4: \(y=x^2+7x+12\)