Converting a vertex form to a factored form can be achieved using a similar approach to converting from the factored form to the vertex form. To demonstrate, we are going to start with an example of an equation.
$$y=(x+3.5)^2-0.25$$
First of all, you need to see if there is a factored form. There is a factored form if the $k$ value of the expression is negative, and the $a$ value is positive, or the $k$ value is positive and the $a$ value is negative. As the $a$ and $k$ values are 1 and -0.25 respectively, it is possible to factorize this expression.
The $k$ value (-0.25) is the $y$ value of the vertex, and the x-intercepts (which are defined in the factored form) are where the value of the $y$ is 0. Therefore the difference between these values is the distance that the parabola must travel in order for the vertex to meet the x-intercepts. We also have to account for the $a$ value of the expression, which describes the stretch of the parabola. We use both of these to calculate the effective change in the $y$ value between the $x$ value of the vertex and the $x$ value of the x-intercepts. Lastly, since the change in the $y$ value is defined based on the square of the change in the $x$ value, and we are identifying the change in $x$ value from a given change in $y$, we also need to find the square root of our adjusted change in $y$ value. This gives us an equation of (Eq. 2) to determine the difference in $x$ value between our vertex and our $x$ intercepts.
$$\sqrt{1(0-(-0.25))}=0.5$$
Once we have the change in $x$ required for the parabola to meet the x-axis from the vertex, we have to identify where these x-intercepts are. To do this, we have to add and subtract this change in $x$ value to and from the $x$ value of the vertex. To get the $x$ value of the vertex, we use the inverse of the $h$ value of the vertex form (-3.5).
$$-3.5+0.5=-3$$ $$-3.5-0.5=-4$$
This leaves 2 x-intercepts which can be placed into the factored form of the equation. The x-intercepts are in the factored form of the equation as the values which added or subtracted from the $x$ terms, where the values are the inverse of the x-intercepts.
$$(x+3)(x+4)$$
This makes the final factored form of the quadratic expression from the vertex form.