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Absolute Value

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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  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 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

  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: 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)

  5. Graph of Parent Function & Example Parent: Y=|x| Equation after shift: Y=|x-3|-2 Shift: 3 Right 2 Down Parent After shift

  6. 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.

  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: |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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