Problem 69 - College Algebra

Question

What is a parabola?

Step-by-Step Solution

Answer

A parabola is a U-shaped, symmetric curve on a plane, described by the equation \(y = ax^2 + bx + c\). All points on the parabola are equidistant from a point called the focus and a line called the directrix.

Step 1: Definition

A parabola is a U-shaped symmetrical curve on a plane. It can be categorized into different parts: vertex, axis of symmetry, focus, and directrix.

Step 2: Mathematical Representation

A parabola can be mathematically represented in the form \(y = ax^2 + bx + c\) where \(a\), \(b\), and \(c\) are constants.

Step 3: Properties of Parabola

Some important properties of a parabola include that it is symmetric with respect to its vertical axis, the vertex represents the minimum or maximum point, all points on the parabola are equidistant from the focus and the directrix.