Absolute value
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Absolute Value PowerPoint PPT Presentation


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Absolute Value. By: Katie Harbeck, Huy Nguyen, Myle Nguyen, Julie Pham. Welcome to the absolute value lesson. 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. Example:.

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Absolute Value

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Absolute value

Absolute Value

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


Welcome to the absolute value lesson

Welcome to the absolute value lesson

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


Example

Example:

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

The slope is one on either side.

The Vertex

(3 ,- 2)

(H,K)


Parent function shifting

Parent Function & Shifting

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)


Graph of parent function example

Graph of Parent Function & Example

Parent: Y=|x|

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

Shift:

3 Right

2 Down

Parent

After shift


Slope of the equation

Slope of the Equation

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.


Example1

Example:

When the value of a is negative

When the value of a is positive


Example2

Example:

When the value of a is greater than 1

When the value of a is less than 1


Hints

Hints

  • 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


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