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Graphing Absolute Value Equations

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Graphing Absolute Value Equations. How do I make one of those V graphs? ... There is only one y value that will only have one x value and that is called the ... – PowerPoint PPT presentation

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Title: Graphing Absolute Value Equations


1
Graphing Absolute Value Equations
  • How do I make one of those V graphs?

2
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)

3
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
4
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

5
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)

6
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

7
How do I graph the equation cont.
  • Lastly, plot the points and connect them forming
    a V or /\

8
Example
  • Find vertex x 1 0 x 1

vertex
(1, 2)
9
Example
vertex
  • Find x-coordinates to left and right, then
  • solve for y- coordinate

(1, 2)
Left of vertex
Right of vertex
10
Example
  • Plot the points
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