Absolute Value

1
Absolute Value

• By Katie Harbeck, Huy Nguyen, Myle Nguyen, Julie
  Pham

2
Welcome to the absolute value lesson

• The equation of absolute value is Yax - h k
• A represents slope
• X is the independent variable
• H is the X value of the vertex
• K is the Y value of the vertex

3
Example

• The equation is y 1 x -3 -2

The slope is one on either side.
The Vertex (3 ,- 2) (H,K)
4
Parent Function Shifting

• The parent function of any absolute value
  equation is Yx
• The H value in the equation moves the graph left
  or right
• The K value in the equation moves the graph up or
  down
• The A value in the equation dictates the degree
  of change in the graph and its position (
  pointing up or down)

5
Graph of Parent Function Example
Parent Yx Equation after shift
Yx-3-2 Shift 3 Right 2 Down
Parent
After shift
6
Slope of the Equation

• In the equation Yax-hk , a represents the
  slope of the graph.
• The value of a determines whether the graph
  points up or down.
• When a is positive, then the graph points up.
• If a is negative, the graph points down.
• The value of a also determines the width of the
  graph.
• When the value of a is less than 1, the graph
  will be wider.
• When the value of a is greater than 1, the graph
  will be thinner.

7
Example
When the value of a is negative
When the value of a is positive
8
Example
When the value of a is greater than 1
When the value of a is less than 1
9
Hints

• Incase!
• are absolute value lines, to calculate the
  number within them it is how many places from
  zero
• Example 3157631576, -3157631576
• Common mistake
• Example yx3-2 In this shifting it is 3 left,
  2 down. Even though the 3 looks positive it
  isn't, because the equation is yax-hk and a
  negative and a negative makes a positive.
• Remember other uses of shifting
• Shifting with other equations is exactly the same
  
• Example Quadratics Ya(x-h)2k