Absolute Value Equations,Circles, and their graphs

Circles


This is the graphing form of a circle graph.


This is the standard form of a circle graph.


Here is an example of an equation that will be graphed as a circle.




cw3-5.png

To Find the Radius and Vertex from an Equation in Graphing Form



When you look at this equation you see x-4, so 'h' has to be 4, then if you look at y-3, 'k' would have to be 3. So the vertex of the circle would be at (4,3). The the radius is 2.

Another Example





Vertex= (h,k)-->(3,3)
Radius=(r)-->4


Absolute Value


Absolute value is the value at that represents how far away from zero a number is. For example, the absolute value of denoted |x| = 5, x can be 5 or -5, because -5 and 5 are both 5 digits away from 0. The same can be applied with |x| = 10, value of x can be 10 or -10, because -10 and 10 are both 10 digits away from zero.

The formula for an absolute value is f(x) = a(|x-h|)+k

When graphing an absolute value, the graph is always a V.

Absolute_value.png



Key For Moving Absolute Value graphs.
Using 1 and 2 as substitutes

Move Up: |x|+1
Down: |x|-1
Stretch: |x|/2
Compress: 2|x|
Move Right: |x-1|
Move Left: |x+1|