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Converting Vertex Form to Factored Form

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 we can follow the process to convert to a standard form.

$$y=(x+3.5)^2-0.25$$

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

$$y=(x+3.5)(x+3.5)-0.25$$

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.

$$y=x^2+3.5x+3.5x+12.25-0.25$$

Like terms can then be combined to give the expression in the standard form.

$$y=x^2+7x+12$$