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Chapter 2: Problem 78

What is a parabola? Describe its shape.

Short Answer

Expert verified
A parabola is a curve in mathematics that is shaped symmetrically and opens upwards or downwards (or sideways), with a highest or lowest point known as the vertex. It is defined as the set of all points equidistant from a fixed point (focus) and a fixed line (directrix). The curve steepens as you move further from the vertex, and the parabola has an axis of symmetry.

Step by step solution

01

Understanding a Parabola

A parabola is a curved line that is used in mathematics. It is defined as the set of all points in the plane equidistant from a fixed point named the focus, and a fixed line called the directrix.
02

Describing the Shape of a Parabola

The shape of a parabola, when graphed, is a curve that opens upwards or downwards (or left or right, depending on the orientation). It is symmetrical, meaning that it appears the same on either side when you draw a line through its vertex, which is its highest or lowest point. As one moves further from the vertex, the curve steepens.
03

Unique Properties of a Parabola

The two unique properties of a parabola are also important to mention. Firstly, the parabola has a vertex which is either the highest or lowest point of the parabola. Secondly, it has an axis of symmetry which is the line that cuts the parabola into two symmetrical halves.

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