Master Graphing and Absolute Value Equations
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Master Graphing and Absolute Value Equations

From basic to the most advanced you will learn how to graph absolute value equations.
4.5 (1 rating)
Instead of using a simple lifetime average, Udemy calculates a course's star rating by considering a number of different factors such as the number of ratings, the age of ratings, and the likelihood of fraudulent ratings.
30 students enrolled
Last updated 10/2014
English
Price: $20
30-Day Money-Back Guarantee
Includes:
  • 1.5 hours on-demand video
  • 2 Supplemental Resources
  • Full lifetime access
  • Access on mobile and TV
What Will I Learn?
  • Students will be able to identify the vertex and axis of symmetry for an absolute value equation
  • Students will be able to graph an Absolute Value Equation with a horizontal translation
  • Students will be able to graph an Absolute Value Equation with a vertical translation
  • Students will be able to graph an Absolute Value Equation with reflections
  • Students will be able to graph an Absolute Value Equation with a compression and stretch
  • Students will be able to graph an Absolute Value Equation by transforming the parent graph
  • Students will be able to graph an Absolute Value Equation by using a table of values and axis of symmetry
View Curriculum
Requirements
  • Transformations of functions
  • Graphing functions from a table of values
Description

Math is life – everything we do in our day-to-day lives involves math in some way, whether we realize it or not. Graphing Absolute Value Equations is definitely not an exception, and understanding how to do it will open up a world of graphic solutions, algebraic processes, and even life solutions.

But none of that means anything if you don’t have an easy way of understanding it. That’s where this three-part course comes in.

Introduction – To start things out, I’ll use sample videos and worksheets to give you simple definitions, process outlines, and some basic questions to help you build up an understanding of how to graph Absolute Value Equations. Even if you’ve tried to learn this before, we’ll start from scratch to get you on the right foot.

Examples – Understanding is all about applying and testing, so next you’ll work through some examples to help drive in what you learned in the first section about graphing Absolute Value Equations. This isn’t about getting a passing grade, so there’s no stress to get everything right. Complete the whole worksheet if you can, or just pick the problems you know you need to work on, and check your answers against a short step-by-step tutorial that shows you how to get from problem to solution.

Conclusion – Finally, you’ll get another worksheet of questions to discuss, reflect on, and answer to really drive in what you’ve learned and ensure you’ve got it in the long run. For those who want to move on to the next course, there are even challenge problems to get you ready. But mostly, this section is about making sure you’re ready for real-world application, not just finishing a worksheet. It’ll all come together in a final summary video where I point out common mistakes plus tips and little-known tricks to help you along in the future when graphing absolute value equations.

This course should only take a couple days, but what you learn will help you for the rest of your life. All at a tiny fraction of what a tutor would cost, and right from the comfort of a home laptop, tablet, or phone. No driving, no anxiety, no pressure, all for under $10 with a 30-day money-back guarantee.

See how much simpler math can be. Sign up today to get started!

Who is the target audience?
  • Algebra 2 Students
  • College Algebra Students
  • Anyone willing to learn
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Curriculum For This Course
24 Lectures
01:22:34
+
Introduction
2 Lectures 03:07

This video is designed to show you everything you should know before starting this course. We will review the essential skills and definitions needed to be successful for this course.

Preview 03:07

Essential Questions are here to give you an idea of what we are trying to learn within this course. The essential questions are also designed to have to learn the material in this course rather than just solving problems.

Essential Questions
1 page
+
Essential Definitions and Processes
4 Lectures 16:45

The parent graph of an absolute function is commonly know as the V graph after it's shape. We call it the parent graph because if s the true form of the graph without any transformations. We will use this graph when graphing other absolute value equations with transformations.

Preview 03:38

The transformations for the absolute value equation follow the transformations for the family of functions. The transformation equations for an absolute value equation are y=(a)abs(x-h)+k and y=(a)abs(bx-h)+k. Where h translates the graph horizontally and k translates the graph vertically. It is also the new coordinates of vertex (h,k). A stretches the graph horizontally when 0<a<1 and compresses the graph horizontally when a>1. The same compression and stretching is applied to the value of b. A reflects the graph over the x-axis and b reflects over the y-axis.

Preview 07:25

The most common characteristic of the absolute value equation is it's v-shaped graph. There are many important parts about the V-shaped graph that will be useful when graphing absolute value equations. First of all is the vertex of the V shaped graph. This is the point where the graph "rebound" in it's slope. It is also noted as the minimum or maximum point on the graph depending on the opening of the graph and called the vertex. Notice how the graph is symmetric on both sides of this graph. We describe the vertical line that runs through the vertex of an absolute value equation the axis of symmetry. Lastly we will look at the characteristics of the slopes for the parent graph of the absolute value equation. The slope in the positive direction is 1 and in the negative direction is -1

What are the characteristics of an absolute value equation
03:14

When graphing absolute value inequalities we first need to graph absolute value equations by applying the transformations of the equation to the parent graph. We first plot the new vertex by identifying the horizontal and vertical shift of the equation. We then create a table of values to plot the points to one side of the vertex to account for the horizontal compression, stretch and reflection of the graph. Then reflect the points over the axis of symmetry to create the graph. Before graphing the line we will need to determine if the points on the graph are apart of the solution or not. To do this we can test a point on the graph. If that point makes the inequality true then it is apart of the solution. When we have a graph that is solid. If the graph is not apart of the solution then we graph the equation as dashed. We can also look at the original inequality symbol when it is less than or greater than then it is dashed. Greater than or equal to and less than or equal to produces a solid graph. Lastly we need to determine if the points above the graph or the points below the graph are apart of the solution. To do this we need to choose a point that is either above or below the line and is not on the line. The best point to choose if available is (0,0). If the test point is true below the line then all of the points below the graph are true so we will shade below the line. If the point is false then we will shade above the line.

How do we graph an absolute value equation
02:28
+
Examples
17 Lectures 55:00
Problems
1 page

When graphing absolute value inequalities we first need to graph absolute value equations by applying the transformations of the equation to the parent graph. We first plot the new vertex by identifying the horizontal and vertical shift of the equation. We then create a table of values to plot the points to one side of the vertex to account for the horizontal compression, stretch and reflection of the graph. Then reflect the points over the axis of symmetry to create the graph. Before graphing the line we will need to determine if the points on the graph are apart of the solution or not. To do this we can test a point on the graph. If that point makes the inequality true then it is apart of the solution. When we have a graph that is solid. If the graph is not apart of the solution then we graph the equation as dashed. We can also look at the original inequality symbol when it is less than or greater than then it is dashed. Greater than or equal to and less than or equal to produces a solid graph. Lastly we need to determine if the points above the graph or the points below the graph are apart of the solution. To do this we need to choose a point that is either above or below the line and is not on the line. The best point to choose if available is (0,0). If the test point is true below the line then all of the points below the graph are true so we will shade below the line. If the point is false then we will shade above the line.

Graphing Absolute Value Equations ex 1
02:13

When graphing absolute value inequalities we first need to graph absolute value equations by applying the transformations of the equation to the parent graph. We first plot the new vertex by identifying the horizontal and vertical shift of the equation. We then create a table of values to plot the points to one side of the vertex to account for the horizontal compression, stretch and reflection of the graph. Then reflect the points over the axis of symmetry to create the graph. Before graphing the line we will need to determine if the points on the graph are apart of the solution or not. To do this we can test a point on the graph. If that point makes the inequality true then it is apart of the solution. When we have a graph that is solid. If the graph is not apart of the solution then we graph the equation as dashed. We can also look at the original inequality symbol when it is less than or greater than then it is dashed. Greater than or equal to and less than or equal to produces a solid graph. Lastly we need to determine if the points above the graph or the points below the graph are apart of the solution. To do this we need to choose a point that is either above or below the line and is not on the line. The best point to choose if available is (0,0). If the test point is true below the line then all of the points below the graph are true so we will shade below the line. If the point is false then we will shade above the line.

Graphing Absolute Value Equations ex 2
01:57

When graphing absolute value inequalities we first need to graph absolute value equations by applying the transformations of the equation to the parent graph. We first plot the new vertex by identifying the horizontal and vertical shift of the equation. We then create a table of values to plot the points to one side of the vertex to account for the horizontal compression, stretch and reflection of the graph. Then reflect the points over the axis of symmetry to create the graph. Before graphing the line we will need to determine if the points on the graph are apart of the solution or not. To do this we can test a point on the graph. If that point makes the inequality true then it is apart of the solution. When we have a graph that is solid. If the graph is not apart of the solution then we graph the equation as dashed. We can also look at the original inequality symbol when it is less than or greater than then it is dashed. Greater than or equal to and less than or equal to produces a solid graph. Lastly we need to determine if the points above the graph or the points below the graph are apart of the solution. To do this we need to choose a point that is either above or below the line and is not on the line. The best point to choose if available is (0,0). If the test point is true below the line then all of the points below the graph are true so we will shade below the line. If the point is false then we will shade above the line.

Graphing Absolute Value Equations ex 3
02:47

When graphing absolute value inequalities we first need to graph absolute value equations by applying the transformations of the equation to the parent graph. We first plot the new vertex by identifying the horizontal and vertical shift of the equation. We then create a table of values to plot the points to one side of the vertex to account for the horizontal compression, stretch and reflection of the graph. Then reflect the points over the axis of symmetry to create the graph. Before graphing the line we will need to determine if the points on the graph are apart of the solution or not. To do this we can test a point on the graph. If that point makes the inequality true then it is apart of the solution. When we have a graph that is solid. If the graph is not apart of the solution then we graph the equation as dashed. We can also look at the original inequality symbol when it is less than or greater than then it is dashed. Greater than or equal to and less than or equal to produces a solid graph. Lastly we need to determine if the points above the graph or the points below the graph are apart of the solution. To do this we need to choose a point that is either above or below the line and is not on the line. The best point to choose if available is (0,0). If the test point is true below the line then all of the points below the graph are true so we will shade below the line. If the point is false then we will shade above the line.

Graphing Absolute Value Equations ex 4
01:57

When graphing absolute value inequalities we first need to graph absolute value equations by applying the transformations of the equation to the parent graph. We first plot the new vertex by identifying the horizontal and vertical shift of the equation. We then create a table of values to plot the points to one side of the vertex to account for the horizontal compression, stretch and reflection of the graph. Then reflect the points over the axis of symmetry to create the graph. Before graphing the line we will need to determine if the points on the graph are apart of the solution or not. To do this we can test a point on the graph. If that point makes the inequality true then it is apart of the solution. When we have a graph that is solid. If the graph is not apart of the solution then we graph the equation as dashed. We can also look at the original inequality symbol when it is less than or greater than then it is dashed. Greater than or equal to and less than or equal to produces a solid graph. Lastly we need to determine if the points above the graph or the points below the graph are apart of the solution. To do this we need to choose a point that is either above or below the line and is not on the line. The best point to choose if available is (0,0). If the test point is true below the line then all of the points below the graph are true so we will shade below the line. If the point is false then we will shade above the line.

Graphing Absolute Value Equations ex 5
02:53

When graphing absolute value inequalities we first need to graph absolute value equations by applying the transformations of the equation to the parent graph. We first plot the new vertex by identifying the horizontal and vertical shift of the equation. We then create a table of values to plot the points to one side of the vertex to account for the horizontal compression, stretch and reflection of the graph. Then reflect the points over the axis of symmetry to create the graph. Before graphing the line we will need to determine if the points on the graph are apart of the solution or not. To do this we can test a point on the graph. If that point makes the inequality true then it is apart of the solution. When we have a graph that is solid. If the graph is not apart of the solution then we graph the equation as dashed. We can also look at the original inequality symbol when it is less than or greater than then it is dashed. Greater than or equal to and less than or equal to produces a solid graph. Lastly we need to determine if the points above the graph or the points below the graph are apart of the solution. To do this we need to choose a point that is either above or below the line and is not on the line. The best point to choose if available is (0,0). If the test point is true below the line then all of the points below the graph are true so we will shade below the line. If the point is false then we will shade above the line.

Graphing Absolute Value Equations ex 6
02:22

When graphing absolute value inequalities we first need to graph absolute value equations by applying the transformations of the equation to the parent graph. We first plot the new vertex by identifying the horizontal and vertical shift of the equation. We then create a table of values to plot the points to one side of the vertex to account for the horizontal compression, stretch and reflection of the graph. Then reflect the points over the axis of symmetry to create the graph. Before graphing the line we will need to determine if the points on the graph are apart of the solution or not. To do this we can test a point on the graph. If that point makes the inequality true then it is apart of the solution. When we have a graph that is solid. If the graph is not apart of the solution then we graph the equation as dashed. We can also look at the original inequality symbol when it is less than or greater than then it is dashed. Greater than or equal to and less than or equal to produces a solid graph. Lastly we need to determine if the points above the graph or the points below the graph are apart of the solution. To do this we need to choose a point that is either above or below the line and is not on the line. The best point to choose if available is (0,0). If the test point is true below the line then all of the points below the graph are true so we will shade below the line. If the point is false then we will shade above the line.

Graphing Absolute Value Equations ex 7
03:08

When graphing absolute value inequalities we first need to graph absolute value equations by applying the transformations of the equation to the parent graph. We first plot the new vertex by identifying the horizontal and vertical shift of the equation. We then create a table of values to plot the points to one side of the vertex to account for the horizontal compression, stretch and reflection of the graph. Then reflect the points over the axis of symmetry to create the graph. Before graphing the line we will need to determine if the points on the graph are apart of the solution or not. To do this we can test a point on the graph. If that point makes the inequality true then it is apart of the solution. When we have a graph that is solid. If the graph is not apart of the solution then we graph the equation as dashed. We can also look at the original inequality symbol when it is less than or greater than then it is dashed. Greater than or equal to and less than or equal to produces a solid graph. Lastly we need to determine if the points above the graph or the points below the graph are apart of the solution. To do this we need to choose a point that is either above or below the line and is not on the line. The best point to choose if available is (0,0). If the test point is true below the line then all of the points below the graph are true so we will shade below the line. If the point is false then we will shade above the line.

Graphing Absolute Value Equations ex 8
03:24

When graphing absolute value inequalities we first need to graph absolute value equations by applying the transformations of the equation to the parent graph. We first plot the new vertex by identifying the horizontal and vertical shift of the equation. We then create a table of values to plot the points to one side of the vertex to account for the horizontal compression, stretch and reflection of the graph. Then reflect the points over the axis of symmetry to create the graph. Before graphing the line we will need to determine if the points on the graph are apart of the solution or not. To do this we can test a point on the graph. If that point makes the inequality true then it is apart of the solution. When we have a graph that is solid. If the graph is not apart of the solution then we graph the equation as dashed. We can also look at the original inequality symbol when it is less than or greater than then it is dashed. Greater than or equal to and less than or equal to produces a solid graph. Lastly we need to determine if the points above the graph or the points below the graph are apart of the solution. To do this we need to choose a point that is either above or below the line and is not on the line. The best point to choose if available is (0,0). If the test point is true below the line then all of the points below the graph are true so we will shade below the line. If the point is false then we will shade above the line.

Graphing Absolute Value Equations ex 9
03:53

When graphing absolute value inequalities we first need to graph absolute value equations by applying the transformations of the equation to the parent graph. We first plot the new vertex by identifying the horizontal and vertical shift of the equation. We then create a table of values to plot the points to one side of the vertex to account for the horizontal compression, stretch and reflection of the graph. Then reflect the points over the axis of symmetry to create the graph. Before graphing the line we will need to determine if the points on the graph are apart of the solution or not. To do this we can test a point on the graph. If that point makes the inequality true then it is apart of the solution. When we have a graph that is solid. If the graph is not apart of the solution then we graph the equation as dashed. We can also look at the original inequality symbol when it is less than or greater than then it is dashed. Greater than or equal to and less than or equal to produces a solid graph. Lastly we need to determine if the points above the graph or the points below the graph are apart of the solution. To do this we need to choose a point that is either above or below the line and is not on the line. The best point to choose if available is (0,0). If the test point is true below the line then all of the points below the graph are true so we will shade below the line. If the point is false then we will shade above the line.

Graphing Absolute Value Equations ex 10
04:09

When graphing absolute value inequalities we first need to graph absolute value equations by applying the transformations of the equation to the parent graph. We first plot the new vertex by identifying the horizontal and vertical shift of the equation. We then create a table of values to plot the points to one side of the vertex to account for the horizontal compression, stretch and reflection of the graph. Then reflect the points over the axis of symmetry to create the graph. Before graphing the line we will need to determine if the points on the graph are apart of the solution or not. To do this we can test a point on the graph. If that point makes the inequality true then it is apart of the solution. When we have a graph that is solid. If the graph is not apart of the solution then we graph the equation as dashed. We can also look at the original inequality symbol when it is less than or greater than then it is dashed. Greater than or equal to and less than or equal to produces a solid graph. Lastly we need to determine if the points above the graph or the points below the graph are apart of the solution. To do this we need to choose a point that is either above or below the line and is not on the line. The best point to choose if available is (0,0). If the test point is true below the line then all of the points below the graph are true so we will shade below the line. If the point is false then we will shade above the line.

Graphing Absolute Value Equations ex 11
04:32

When graphing absolute value inequalities we first need to graph absolute value equations by applying the transformations of the equation to the parent graph. We first plot the new vertex by identifying the horizontal and vertical shift of the equation. We then create a table of values to plot the points to one side of the vertex to account for the horizontal compression, stretch and reflection of the graph. Then reflect the points over the axis of symmetry to create the graph. Before graphing the line we will need to determine if the points on the graph are apart of the solution or not. To do this we can test a point on the graph. If that point makes the inequality true then it is apart of the solution. When we have a graph that is solid. If the graph is not apart of the solution then we graph the equation as dashed. We can also look at the original inequality symbol when it is less than or greater than then it is dashed. Greater than or equal to and less than or equal to produces a solid graph. Lastly we need to determine if the points above the graph or the points below the graph are apart of the solution. To do this we need to choose a point that is either above or below the line and is not on the line. The best point to choose if available is (0,0). If the test point is true below the line then all of the points below the graph are true so we will shade below the line. If the point is false then we will shade above the line.

Graphing Absolute Value Equations ex 12
03:49

When graphing absolute value inequalities we first need to graph absolute value equations by applying the transformations of the equation to the parent graph. We first plot the new vertex by identifying the horizontal and vertical shift of the equation. We then create a table of values to plot the points to one side of the vertex to account for the horizontal compression, stretch and reflection of the graph. Then reflect the points over the axis of symmetry to create the graph. Before graphing the line we will need to determine if the points on the graph are apart of the solution or not. To do this we can test a point on the graph. If that point makes the inequality true then it is apart of the solution. When we have a graph that is solid. If the graph is not apart of the solution then we graph the equation as dashed. We can also look at the original inequality symbol when it is less than or greater than then it is dashed. Greater than or equal to and less than or equal to produces a solid graph. Lastly we need to determine if the points above the graph or the points below the graph are apart of the solution. To do this we need to choose a point that is either above or below the line and is not on the line. The best point to choose if available is (0,0). If the test point is true below the line then all of the points below the graph are true so we will shade below the line. If the point is false then we will shade above the line.

Graphing Absolute Value Equations ex 13
06:01

When graphing absolute value inequalities we first need to graph absolute value equations by applying the transformations of the equation to the parent graph. We first plot the new vertex by identifying the horizontal and vertical shift of the equation. We then create a table of values to plot the points to one side of the vertex to account for the horizontal compression, stretch and reflection of the graph. Then reflect the points over the axis of symmetry to create the graph. Before graphing the line we will need to determine if the points on the graph are apart of the solution or not. To do this we can test a point on the graph. If that point makes the inequality true then it is apart of the solution. When we have a graph that is solid. If the graph is not apart of the solution then we graph the equation as dashed. We can also look at the original inequality symbol when it is less than or greater than then it is dashed. Greater than or equal to and less than or equal to produces a solid graph. Lastly we need to determine if the points above the graph or the points below the graph are apart of the solution. To do this we need to choose a point that is either above or below the line and is not on the line. The best point to choose if available is (0,0). If the test point is true below the line then all of the points below the graph are true so we will shade below the line. If the point is false then we will shade above the line.

Graphing Absolute Value Equations ex 14
04:55

When graphing absolute value inequalities we first need to graph absolute value equations by applying the transformations of the equation to the parent graph. We first plot the new vertex by identifying the horizontal and vertical shift of the equation. We then create a table of values to plot the points to one side of the vertex to account for the horizontal compression, stretch and reflection of the graph. Then reflect the points over the axis of symmetry to create the graph. Before graphing the line we will need to determine if the points on the graph are apart of the solution or not. To do this we can test a point on the graph. If that point makes the inequality true then it is apart of the solution. When we have a graph that is solid. If the graph is not apart of the solution then we graph the equation as dashed. We can also look at the original inequality symbol when it is less than or greater than then it is dashed. Greater than or equal to and less than or equal to produces a solid graph. Lastly we need to determine if the points above the graph or the points below the graph are apart of the solution. To do this we need to choose a point that is either above or below the line and is not on the line. The best point to choose if available is (0,0). If the test point is true below the line then all of the points below the graph are true so we will shade below the line. If the point is false then we will shade above the line.

Graphing Absolute Value Equations ex 15
02:56

When graphing absolute value inequalities we first need to graph absolute value equations by applying the transformations of the equation to the parent graph. We first plot the new vertex by identifying the horizontal and vertical shift of the equation. We then create a table of values to plot the points to one side of the vertex to account for the horizontal compression, stretch and reflection of the graph. Then reflect the points over the axis of symmetry to create the graph. Before graphing the line we will need to determine if the points on the graph are apart of the solution or not. To do this we can test a point on the graph. If that point makes the inequality true then it is apart of the solution. When we have a graph that is solid. If the graph is not apart of the solution then we graph the equation as dashed. We can also look at the original inequality symbol when it is less than or greater than then it is dashed. Greater than or equal to and less than or equal to produces a solid graph. Lastly we need to determine if the points above the graph or the points below the graph are apart of the solution. To do this we need to choose a point that is either above or below the line and is not on the line. The best point to choose if available is (0,0). If the test point is true below the line then all of the points below the graph are true so we will shade below the line. If the point is false then we will shade above the line.

Graphing Absolute Value Equations ex 16
04:04
+
Conclusion
1 Lecture 05:42

In this video I will summarize the process for solving one-step equations as well as provide common mistakes and helpful tips and tricks that have helped myself and fellow students.

Summary
05:42
About the Instructor
Brian McLogan
4.5 Average rating
32 Reviews
882 Students
8 Courses
Current Active High School Math Teacher

I am a high school that is on a mission to improve math education. I was that student that sat in the back of class frustrated with the boredom of class and the lack of understanding. I made the decision to become a math teacher to make a difference in others lives. I knew that with the struggles I had I could relate well to students that struggled with math. With a weak math background I set out to get a degree in mathematics. In was a difficult journey and I worked very hard not just to pass my math classes but to have an understanding of what I was doing. I learned a lot about myself, mathematics and what it takes to be successful in class through my time at college. I want to pass along my experience to you the student so that may have your own success with mathematics.

Shalom Love B Tablando
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