graphing absolute value equations how do i make one of those v graphs?
TRANSCRIPT
Graphing Absolute Value Equations
How do I make one of those V graphs?
What does the graph look like?
V
Minima – lowest point of graph
Vertex = minima Sides are linear
/\
Maxima – highest point of graph
Vertex = maxima Sides are linear
vertex
How do I graph the Equation?
X-coordinate of the vertex is the value of
Plug in the value of x and solve for y
This the ordered pair for the vertex(x,y)
cbxay
0bx
How do I graph the equation cont.
Next, find x values to the left of the vertex and to the right of the vertex
Solve for the y values
cbxay
How do I graph the equation cont.
Lastly, plot the points and connect them forming a V or /\
cbxay
vertex(1, 2)
Example
1. Find vertex x – 1 = 0 x = 1
21 xy
2
211
y
y
vertex
Example
Find x-coordinates to left and right, then
solve for y- coordinate
21 xy
3
21
210
y
y
y
(1, 2)
X -1 0 1 2 3
Y 4 3 2 3 4
4
22
211
y
y
y
3
21
212
y
y
y
4
22
213
y
y
y
Left of vertex
Right of vertex
Example
Plot the points
21 xy
X -1 0 1 2 3
Y 4 3 2 3 4
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
-1 0 1 2 3
Absolute ValueEquation
Translations
Parent Function
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
-1 0 1 2 3
Absolute ValueEquation
xy
More Translations
Vertical Translation Up
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
-1 0 1 2 3
Absolute ValueEquation
kxy
Even More Translations
Vertical Translation Down
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
-1 0 1 2 3
Absolute ValueEquation
kxy
Yet, Even More Translations
Horizontal Translation Left
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
-1 0 1 2 3
Absolute ValueEquation
kxy
Again…Translations
Horizontal Translation Right
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
-1 0 1 2 3
Absolute ValueEquation
kxy
Translations….
Vertical Compression (Think Slope) a>1
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
-1 0 1 2 3
Absolute ValueEquation
xay
Will the Translations End??!
Vertical Stretch (Think Slope) a<1
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
-1 0 1 2 3
Absolute ValueEquation
xay
Finally, the Last Translation
Reflection (Think Slope) a<0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
-1 0 1 2 3
Absolute ValueEquation
xay
Recap
khxay