2-5 and 2-6 Graphing Absolute Value Equations

8/6/2019 2-5 and 2-6 Graphing Absolute Value Equations

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Graphing Absolute ValueEquations



Absolute Value Equation

A V-shaped graph that points upward or downward is the graph of an absolutevalue equation.

Translation A translation is a shift of a graph

horizontally, vertically or diagonally(combination of vertical and horizontaltranslation).



Graphing Absolute Value Equations

Vertical TranslationThe graph of y = x + k is a translation of y = x .

if k is positive up k unitsif k is negative down k units

Horizontal Translation

The graph of y = x ±h

is a translation of y = x .if h is positive right h unitsif h is negative left h units




Diagonal Translation A combination of vertical and horizontal

translation.

The graph of y = x ± h + k is a translation

of y = x .




Example 1: Graph the absolute value equationy = x - 5.

Solution:

Step 1. Press y = key on you calculator.Step 2. Use the NUM feature of MATH screen on your graphing calculator.

Step 3. Choose 1: abs( feature on you calculator.Step 4. Enter the given equation.

X,,,n , ) , - , 5

Step 5. Press GRAPH.



Cont (example 1)«

6

10

1

8 6 0 6 8



Do these«

Graph each function. Identify the vertex of eachfunction.

1. y = x + 22. y = x - 4 3. y = x - -2

4. y = x - 2+ 1.



Answers:

1. 2.

3. 4.



Writing an Absolute Value Equation

Write an equation for each translation of y = xExample 1: 9 units up

9 units up is vertical translation so use

y = x + k S ince k is positive, the equation is

y = x + 9Example 2: 2 units down

2 units down is vertical translation so usey = x + kSince k is negative, the equation is

y = x - 2




Write an equation for each translation of y = -x.Example 3: 5 units right

5 units right is horizontal translation so use

y = -x - hS ince k is positive, the equation is

y = -x - 5Example 4: 3 units left

3 units left is horizontal translation so usey = -x -hSince k is negative, the equation is

y = -x ± (-3) y = -x +3




Write an equation for each translation of y = x.Example 5: 2 units up and 1 unit leftsince this involves horizontal and vertical translations use

y = x - h+ k S ince k is positive and h is negative, the equation is

y = x ± (-1)+ 2 y = x +1+ 2Example : 5 units down and 4 units left

since this involves horizontal and vertical translations usey = x - h+ k

Since k is negative and h is negative, the equation isy = x ± (-4)+ (-5) y = x +4 - 5



Do these«

Write an equation for each translation of the parent function y = ©x©.

1. Left 9 units2. Right 2 unit3. Up 1 unit

4. Down 2/3 unit5. Left 3 units and down 4 units. Right 5 units and up 1 unit

Answers: 1. y = x + 92. y = x - 23. y = x + 1

4. y = x - 2/35. y = x +3- 4

6 . y = x - 5 + 1



Graph each absolute value equation thendescribe the translation of the parent

function.

Example 1. y = ©x - 7© + 2

Answer: y = ©x©is translated 7 units to theright and 2 units up.

Describing a Translation



Describing a Translation

Graph each absolute value equation thendescribe the translation of the parent

function.

Example 2. y = -©x + 3© - 1

Answer: y = -©x©is translated 3 units to theleft and 1 unit down.



Do these«

Graph each absolute value equation then describethe translation of the parent function.

1. y = ©x + 1©- 32. Y = ©x ± 3 © - 13. Y = ©x + 2 ©+ 14. Y = - ©x - 1 © -5. Y = - ©x - 5 ©+ 7



Write the equation of the givengraph.

1

2

3

4

5

7

1 2 3 4 5 7 9

Answer: Since the vertex is at the point (5, 3), thenh= 5 and k = 3. Therefore, the equation is

y = x ± 5+ 3.

2-5 and 2-6 Graphing Absolute Value Equations

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