04-1d+-+Vertices

If a parabola opens upward, it has a minimum point. If the parabola opens downward, it has a maximum point.

We call the lowest or highest point of the parabola the vertex of the parabola.

The parent function, f(x) = x2, has its vertex at the origin.

A very useful form of a quadratic equation is the vertex form of the equation. We can read the coordinates of the vertex of the parabola from the vertex form of the equation. In general terms, the equation looks like this:

﻿ f(x) = a(x - h) 2  + k, where a, h and k are constants



Since the parabola is translated h units horizontally and k units vertically, the coordinates of the vertex are (h, k).

If we reexamine the parent function, we see that a = 1, h = 0 and k = 0, which corresponds to the vertex at the origin.



Narrated Version of the lesson: media type="file" key="Vertex Form 1.swf" width="468" height="351"