Sevenmonkisinidn
Answered

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A parabola has a vertex at [tex]\((0,0)\)[/tex]. The equation for the directrix of the parabola is [tex]\(x = -4\)[/tex].

In which direction does the parabola open?

A. up
B. down
C. right
D. left

Sagot :

GinnyAnsweridn
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.
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