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Graphing Absolute Value Equations

- How do I make one of those V graphs?

Definition of Absolute Value

- x x if x gt 0
- 0 if x 0
- -x if x lt 0
- That way it is always positive or 0

- (x if positive)
- (0 if 0)
- (opposite of x if negative)

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

Why is the graph a V?

- Y xthere are 2 values of x that will work for

every y value. If x 3 and -3, y 3. - There is only one y value that will only have one

x value and that is called the vertex. - The vertex is where the expression insdie the

absolute value symbol is equal to zero

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)

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

How do I graph the equation cont.

- Lastly, plot the points and connect them forming

a V or /\

Example

- Find vertex x 1 0 x 1

vertex

(1, 2)

Example

vertex

- Find x-coordinates to left and right, then
- solve for y- coordinate

(1, 2)

Left of vertex

Right of vertex

Example

- Plot the points

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