31-48 Finding the Equation of a Parabola Find an equation for the parabola that has its vertex at the origin and satisfies the given condition(s).
Directrix has y-intercept .
The equation for the parabola that has its vertex at the origin and the directrix has y-intercept .
The vertex is .
The general equation for a parabola with a vertical axis having the vertex at the origin and the focus is as follows.
Here, is the distance from the origin.
The focus is and the directrix line is
The parabola opens to the right, if or to the left if .
Since, the vertex of the parabola lies halfway between the focus and the directrix.
The figure is plotted as given below.
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