2.8 Absolute Value Equations
RECALL from yesterday’s investigation…
The graph of y = a x − h + k has the following characteristics:
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The graph has a vertex (h , k ) and is symmetric in line x = h.
The graph is V-shaped. If a > 0 it opens up and if a < 0 it opens down.
The graph gets wider than the graph y = |x| if a < 1
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The graph gets narrower than the graph y = |x| if a > 1
To graph
graph an absolute value function:
function:
• plot the vertex and one other point
• use symmetry to plot a third point
• then complete the graph
Ex:
Ex: y = x + 2 + 3
Ex:
Ex: y = − x − 1 + 1
Practice:
Practice
1. y = − | x + 3| +4
2. y = 3| x − 2|
Ex:
Ex: Write an equation for the graphs shown below.
Vertex:
Value of a:
Equation:
Vertex:
Value of a:
Equation:
3. y = − | x | +6
Vertex:
Value of a:
Equation:
Vertex:
Value of a:
Equation:
What do you think the graph of y >|x| would look like? What about
In Calculator:
y = MATH → NUM
1: abs(
Ex: Graph y = |x – 2| – 3
ZOOM 6: Standard
y ≤x ?