Graphing Absolute
Value Functions
Value Functions
Solving Absolute Value Equations
Vocabulary
Absolute Value Transformations
Challenge
100
Identify the vertex and slope of the following function and graph it.
y= |x-3|+4
Vertex : (3,4). Slope: 1
100
Solve the absolute value equation ALGEBRAICALLY
-5|x-10|-15=0
-5 |x - 10| - 15 = 0
+ 15 +15
-5 | x - 10| = 15
(-5|x-10|)/-5= 15/-5
|x-10| = -3
No Solution
100
What is slope?
Rise over run
100
Identify all the transformations for the absolute value function.
y = |x| - 4
Translates down 4 units
100
Push It
Someone does either 20 pushups, sit-ups or arm circles
200
Identify the vertex and slope of the following function and graph it.
y=-|x-4|+1
Vertex: (4,1). Slope: -1
200
Solve the absolute value equation by GRAPHING or ALGEBRAICALLY
|x+1|-4=1
x=-6 and x=4
200
What is Y-intercept?
Where a line crosses the y-axis.
200
Identify all the transformations for the absolute value function.
y = |x + 2| + 10
1. Translates left 2 units
2. Translates up 10 units
300
Identify the vertex and slope of the following function and graph it.
y=2|x+5|-3
Vertex: (-5,-3). Slope: 2
300
Solve the absolute value equation by GRAPHING or ALGEBRAICALLY.
-3|x+3|+3=-3
x = -5 and x = -1
300
Define Vertex
Point on a graph where the graph changes direction!
300
Identify all the transformations for the absolute value function.
y= -| x - 5| + 8
1. Reflects over x-axis
2. Translates right 5 units
3. Translates up 8 units
300
This NBA team is most likely going to win the championship this year.
Oklahoma City Thunder
400
Identify the vertex and slope of the following function and graph it.
y= 3|x+2|-5
Vertex: (-2,-5) Slope: 3
400
Solve the absolute value equation ALGEBRAICALLY
2|x-12|+5 = 15
2|x-12|+5 = 15
-5 -5
2|x-12| = 10
(2|x-12|)/2=10/2
x-12 = 5 x-12 = -5
+12 +12 +12 +12
x = 17 and x = 7
400
Define axis of symmetry
vertical line going through the vertex
400
Identify all the transformations for the absolute value function.
y = 3 | x + 3| - 2
1. Vertical stretch by a factor of 3 (Vertical Scaling / Slope = 3)
2. Translates left 3 units
3. Translates down 2 units
400
What does Bad Bunny's song "DtMF" mean?
"DtMF" is an abbreviation for Bad Bunny's 2025 song and album title, "Debí Tirar Más Fotos," which translates from Spanish to English as "I Should Have Taken More Photos".
500
Identify the vertex and slope of the following function and graph it.
y=-2|x-2|+4
Vertex: (2,4). Slope: -2
500
Solve the absolute value equation ALGEBRAICALLY
4-5|10-5x|=-51
Work will be on the board
x=-1/5 and x= 21/5
500
Absolute Value Vertex Form & what is your vertex?
y = a|x-h|+k
(h,k)
500
Identify all the transformations for the absolute value function.
y= -5|x+6|-11
1. Reflects over x-axis
2. Vertical Stretch by a factor of 5 (Slope is -5, vertical scaling)
4. Translates left 6 units
5. Translates down 11 units
500
This actor known for playing Black Panther, died from colorectal cancer (colon cancer), which he battled privately for four years after being diagnosed with Stage 3 colon cancer in 2016, with it progressing to Stage 4 before his passing in 2020.
Chadwick Boseman