Question

A parabola has a vertex at (0,0). The equation for the directrix of the parabola is x = –4. In which direction does the parabola open? up down right left.

Answer 1

The parabola with vertex at (0,0) and directrix at x=-4, will open towards the right.

What is a directrix?

A parabola is a collection of points on a plane that are all at the same distance from a particular point and line. The point is called the focus of the parabola while the line is called the directrix. The directrix is perpendicular to a parabola's axis of symmetry and does not contact it.

As we know that the directrix is perpendicular to the axis of the parabola, now since the directrix is at x=-4, the parabola will be horizontal and will be opening either towards the left or the right.

As it is given that the vertex of the parabola is at (0,0) and we know that the parabola can not touch the directrix, therefore, the parabola's vertex will be at (0,0) and will open towards the right side. As shown below.

Hence, the parabola with vertex at (0,0) and directrix at x=-4, will open towards the right.

Learn more about Directrix:

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