Question

Describe what the characteristics of a parabola are. Mention symmetry and reasons why parabolas (that open downward) would have symmetry.

Answer 1

A parabola is a symmetrical curve that opens either upward or downward. It has a line of symmetry, a vertex, a focus, a directrix, and an axis of symmetry.

Step-by-step explanation:

A parabola is a type of curve that is formed by the intersection of a plane and a cone. It is a symmetrical curve that opens either upward or downward. The key characteristics of a parabola include:

1. Symmetry: A parabola has a line of symmetry that passes through the vertex. If a parabola opens downward, it has vertical symmetry.
2. Vertex: The vertex is the lowest or highest point on the parabola, depending on its orientation.
3. Focus: The focus is a fixed point inside the parabola, and all the points on the parabola are equidistant from the focus and the directrix.
4. Directrix: The directrix is a fixed line outside the parabola, and the distance from any point on the parabola to the directrix is equal to the distance from that point to the focus.
5. Axis of symmetry: The axis of symmetry is the vertical line passing through the vertex. It divides the parabola into two congruent halves.