Graphing Absolute Value Equations

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Date:
Period:
Topic: Graphing Absolute Value Equations
Warm-Up:
1. Solve the following system of inequalities by
graphing:
y &lt; 2x + 4
- 3x – 2y ≥ 6
2. Which inequality represents the graph below?
a) y &lt; x + 1
b) y ≥ x + 1
c) y ≤ x + 1
d) y &gt; x + 1
Home-Learning Assignment #5
Review
Quiz #8
Graphing Absolute Value
Equations
How do I make one of those V graphs?
Absolute value transformation
Vocabulary:
 Translation: shifts the parent function graph
horizontally and vertically.
 Reflection: it creates a mirror image of the
parent-function graph across the line of
reflection.
Parent Function y = │x │
Vertical Movements?
 Absolute value rules:

If you have minus outside the absolute value,
you move down on the coordinate plane.
y =│x│- 2

If you have addition outside the absolute
value, you move up on the coordinate plane.
y =│x│+ 2
Lets practice!
 y = │x│ - 4
 y = │x│+ 3
 y = │x│ + 7
 y = │x│ - 2
Horizontal Movements?
 Absolute value special rules:

If you have minus inside the absolute value,
you move to the right on the coordinate plane.
y =│x - 2 │

If you have addition inside the absolute value,
you move to the left on the coordinate plane.
y =│x + 2 │
Lets Practice!
 y =│x - 5│
 y =│x + 6│
 y =│x + 4│
 y =│x - 1│
What about y = │x - 4 │+ 5
What about y = -│x - 2 │
y = -│x │
Reflection of the
Parent-function
Same rule, but now it makes it look down
Practice Time!!!
Algebra Aerobics!
1) y = │x - 1│
6) y = │x - 1│+ 2
2) y = │x +3│
7) y = -│x - 6│
3) y = │x │ + 5
8) y = -│x │- 4
4) y = │x│ - 4
9) │x│+ y = - 3
5) y = │x + 3│ + 3
10) y = -│x + 1│ - 1
Mix Algebra Aerobics
y = │x - 4│
y = -│x + 2│ - 2
y ≥ -3x -1
y = -│x - 7│ + 8
y = │x + 5│
x≥4
y≥6
4x + 3y ≤ 24
y = │x │ + 3
Review
Review
Review
Verbal Comprehension Analysis
 Graph the functions y = │x │ and y = │x - 3 │
together on the same coordinate plane.
 What effect does the 3 have on the graph?
 Graph the functions y = │x │ and y = │x │- 3
on the same coordinate plane.
 What effect does the 3 have on the graph?
 Graph the functions y = │x │ and y = - │x │
together on a coordinate plane.
 What effect does the negative sign have on
the graph?
Wrap-up:
 Review key points
 Review vocabulary words
---- Reminder ---Study for Exam #8
(Linear Inequalities, Systems of Inequalities, &amp;
Graphing Absolute Value Equations)
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