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Absolute Value

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Absolute Value

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

The equation of absolute value is Y=a|x - 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

The equation is y = 1 | x -3 |-2

The slope is one on either side.

The Vertex

(3 ,- 2)

(H,K)

The parent function of any absolute value equation is: Y=|x|

- 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)

Parent: Y=|x|

Equation after shift: Y=|x-3|-2

Shift:

3 Right

2 Down

Parent

After shift

In the equation Y=a|x-h|+k , 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.

When the value of a is negative

When the value of a is positive

When the value of a is greater than 1

When the value of a is less than 1

- Incase!
- | | are absolute value lines, to calculate the number within them it is how many places from zero
- Example: |31576|=31576, |-31576|=31576

- Common mistake
- Example: y=|x+3|-2 In this shifting it is 3 left, 2 down. Even though the 3 looks positive it isn't, because the equation is y=a|x-h|+k and a negative and a negative makes a positive.

- Remember other uses of shifting
- Shifting with other equations is exactly the same
- Example : Quadratics: Y=a(x-h)^2+k