2-5: Graphing Absolute Value Functions
Objective:
· To graph any absolute value equation.
Review #1: Graph
using translations
Where is the vertex?
Where is the line of symmetry?
Review #2: Graph
using translations
Where is the vertex?
Where is the line of symmetry?
Review #3: Graph
using translations
Where is the vertex?
Where is the line of symmetry?
Review #4: Graph
using translations
Where is the vertex?
Where is the line of symmetry?
The general shape of an absolute value graph is a " V".
The graphs we have looked at so far have branches that follow the
diagonals on the graph paper.
But sometimes the "V" opens wider or narrower.
Vocabulary:
General Absolute Value Equation:
Vertex:
the minimum or maximum point on an absolute value
graph (the point of the "V")
Line of symmetry:
the vertical line that goes through the vertex and cuts the
the "V" graph in half; it provides reflective symmetry of
the graph
To calculate the line of symmetry:
Set the "insides" of the absolute value = 0 and solve forx.
The equation of this line isx =
To calculate the vertex:
First, calculate the line of symmetry.
The x-coordinate of the vertex is thex-value from the line of symmetry.
Second, substitute thatx-value into the equation and solve fory.
This is the y-coordinate for the vertex.
Always identify the vertex as an ordered pair: (x, y )
To graph the rest of the "V":
Create an x/y table with the vertex in the middle.
Include x values to the left and right of the vertex.
(There should be a total of at least 5x-values.)
Calculate they values by substituting thex-values into the equation.
Plot the 5 points and connect them to make the "V".
EX #1:
Line of Symmetry:
Vertex:
Table:
EX #2:
Line of Symmetry:
Vertex:
Table:
EX #3: Identifying the intercepts:
x-intercept = where a graph crosses the x-axis;
the coordinates for any x-intercept are ( ____ , 0 )
y-intercept = where a graph crosses the y-axis;
the coordinates for any y-intercept are ( 0 , ____ )
If you cannot tell where the x-intercepts are from the graph you will have to
calculate them... just like how we did in Chapter 1.