First, we need to set the given information: the vertex of the parabola is at point (2,-5) and the directrix is x = 23/12.
The focus of the parabola can be found by taking the average between the vertex_x and the directrix. The focus of a parabola is always halfway between the vertex and the directrix.
This gives us:
focus = (vertex_x + directrix) / 2
Next, we need to find the p-value. The p-value of a parabola is defined as the distance from the vertex to the focus. Hence, we subtract the x-coordinate of the vertex from the value of the focus.
p_val = focus - vertex_x
Now we have all the necessary values needed to write the equation of the parabola in transformational form. The standard form of a parabola is:
(x - h)² = 4p(y - k)
where (h, k) is the vertex of the parabola and p is the p-value we found above.
Substituting the values we get:
(x - 2)² = 4*(-0.04166666666666652)(y - -5)
Simplified, this gives us the equation of the parabola in transformational form:
(x - 2)² = -0.1666666666666662 * (y + 5)
This is the equation of the parabola in transformational form with the given vertex and directrix.