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Chapter 3: Problem 75

What is a parabola? Describe its shape.

Short Answer

Expert verified
A parabola is a U- or C-shaped curve that's defined as the set of all points equidistant from a point called the focus and a line called the directrix. Its standard equation is either \(y = ax^2 + bx + c\) or \(x = ay^2 + by + c\).

Step by step solution

01

Definition

A Parabola is a type of curve that is formed by a set of points in a plane that are equidistant from both a given point, called the focus, and a given straight line, called the directrix.
02

Equation

The standard form of a parabola's equation is \(y = ax^2 + bx + c\) or \(x = ay^2 + by + c\) where \(a\), \(b\), and \(c\) are constants.
03

Shape Description

The shape of a parabola is a U-shaped curve that opens either upwards or downwards, or it can be a C-shaped curve that opens either to the right or the left. When the parabola opens upwards or downwards, the vertex of the parabola is the minimum or maximum point. Meanwhile, when the parabola opens towards the right or left, there is no minimum or maximum point.

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