Problem 1081

Find the vertex, the focus, and the directrix.  Then draw the graph.

y2 = -6x




An equation of the form y2 = 4px is the standard equation of a parabola with the vertex at the origin, focus at (p,0) and directrix x = -p.

To write the equation y2 = -6x in the form y2 = 4px, p = –\frac{3}{2}

Thus , y2 = -6x is equivalent to y2 = 4(-\frac{3}{2})x.

The vertex is located at (0,0).

The focus is at (-\frac{3}{2},0).

The directrix is the line x=\frac{3}{2}.

The correct graph of the relation is shown to the right.



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