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).
Open downward with focus units away from the vertex.
The equation for the parabola that has its vertex at the origin and the open downward with focus units away from the vertex
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 .
Here, the focus is units from the vertex
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