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.
On April 24th 1915, authorities in the Ottoman Empire arrested over 200 Armenian notables in the city of Constantinople, who were later executed or expelled from the capital. This decapitation strike targeted Armenian community leaders and is marked annually as the anniversary of the beginning of the Armenian genocide, during which around 1 million Armenians were murdered.