To determine the direction in which the parabola opens, let's analyze the given information step by step.
1. Vertex of the Parabola: The vertex of the parabola is given as [tex]\((0,0)\)[/tex]. This means the parabola is centered at the origin.
2. Directrix of the Parabola: The directrix is given as [tex]\(x = -4\)[/tex]. The directrix is a fixed line, and for a parabola that opens horizontally, it will either be either left or right of the vertex.
3. Nature of the Parabola:
- For a parabola that opens right, the directrix will be on the left side of the vertex.
- For a parabola that opens left, the directrix will be on the right side of the vertex.
Since the directrix [tex]\(x = -4\)[/tex] is to the left of the vertex at [tex]\((0,0)\)[/tex], the parabola must open to the right.
Therefore, the parabola opens to the right.
