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The equation of the vertical parabola in vertex form is written as
Where (h, k) are the coordinates of the vertex and p is the focal distance.
The directrix of a parabola is a line which every point of the parabola is equally distant to this line and the focus of the parabola. The vertex is located between the focus and the directrix, therefore, the distance between the y-coordinate of the vertex and the directrix represents the focal distance.
Using this value for p and (3, 1) as the vertex, we have our equation
Let
x-------> the length side of the original cube
we have
Divide by both sides
The system of equations is equal to
--------> equation
--------> equation
using a graphing tool
see the attached figure
we know that
the solution of the system of equations is the intersection both graphs
therefore
the solution is
therefore
<u>the answer is</u>
