Algebra 1
Unit 2: Graphing Equations
Lesson 10: Graphing Absolute Value Equations
Example 1
Graph: y = |x|
Example 2
Graph: y = |x| +2
Give two solutions to this
equation.
Copyright © 2009-2012 Karin Hutchinson – Algebra-class.com
Algebra 1
Unit 2: Graphing Equations
Example 3
Graph: y = -|x-2| +1
Example 4
Analyze the following graphs.
Y = |1/2x|
(red graph)
Y = |2x| (green graph)
Y = |4x| (yellow graph)
Y = -|4x|
(blue graph)
What do you notice about the
size of the graphs in regards
to the coefficient of x?
Copyright © 2009-2012 Karin Hutchinson – Algebra-class.com
Algebra 1
Unit 2: Graphing Equations
Lesson 10: Graphing Absolute Value Equations and Inequalities – Practice Problems
Part 1: Graph the following absolute value equations and inequalities on the grid.
1 y= |x+2|
2. y = |x-1| +2
3. y = |3x|+1
4. y = |2x+2|
Copyright © 2009-2012 Karin Hutchinson – Algebra-class.com
Identify two solutions.
Algebra 1
Unit 2: Graphing Equations
5. y = |x-1| -3
7. y = -|x-1|
6. y = - |x| +4
Identify two solutions.
8. y = |1/2x| -3
Copyright © 2009-2012 Karin Hutchinson – Algebra-class.com
Algebra 1
Unit 2: Graphing Equations
1. Graph the following inequality on
the grid. (3 points)
Y = |2x-4| -2
2. Identify two solutions.
(2 points)
Copyright © 2009-2012 Karin Hutchinson – Algebra-class.com
Algebra 1
Unit 2: Graphing Equations
Lesson 10: Graphing Absolute Value Equations and Inequalities –Answer Key
Part 1: Graph the following absolute value equations and inequalities on the grid.
1. y= |x+2|
2. y = |x-1| +2
Identify two solutions.
First create a table of values with positive and
negative x values. Then plot the points and
draw your V shaped graph.
First create a table of values with positive and negative x
values. Then plot the points and draw your V shaped
graph.
Two Solutions are: (-3, 6) and (0,3). These are points
on the graph. You can choose any two points on the
graph: (Hint: any point in the table of values is a
solution.)
Copyright © 2009-2012 Karin Hutchinson – Algebra-class.com
Algebra 1
Unit 2: Graphing Equations
3. y = |3x|+1
First create a table of values with positive and
negative x values. Then plot the points and draw
your V shaped graph.
4. y = |2x+2|
First create a table of values with positive and
negative x values. Then plot the points and draw
your V shaped graph.
Copyright © 2009-2012 Karin Hutchinson – Algebra-class.com
Algebra 1
Unit 2: Graphing Equations
5. y= |x-1| -3
6. y = - |x| +4
First create a table of values with positive and
negative x values. Then plot the points and draw
your V shaped graph.
First create a table of values with positive and
negative x values. Then plot the points and draw
your upside down V shaped graph. (This graph is
upside down since we have a negative absolute
value.
Copyright © 2009-2012 Karin Hutchinson – Algebra-class.com
Algebra 1
Unit 2: Graphing Equations
7. y = -|x-1|
Identify two solutions.
First create a table of values with positive and
negative x values. Then plot the points and draw
your upside down V shaped graph.
8. y = |1/2x| -3
First create a table of values with positive and
negative x values. Then plot the points and draw
your V shaped graph.
Two solutions are: (-3,-4) and (-1,-2) (Any
point in the table of values is a solution).
Copyright © 2009-2012 Karin Hutchinson – Algebra-class.com
Algebra 1
Unit 2: Graphing Equations
1. Graph the following inequality on
the grid. (3 points)
Y= |2x-4| -2
2. Identify two solutions. (2 points)
First create a table of values with positive and negative
x values. Then plot the points and draw your V shaped
graph.
Two solutions: (0,2) & (3,0)
values is a solution)
(Any point in the table of
Graphs and table of values were created using a free calculator on rentcalculators.org
Copyright © 2009-2012 Karin Hutchinson – Algebra-class.com