2.8 b absolute value functions

2.8B Absolute Value Functions
Today’s objective:
1. I will check homework:
2.8 Reteaching with Additional Practice.
2.8 Practice B.
2. I will review for Quiz 2 Retake.
3. I will review for Quiz 3
(Piecewise & Absolute Value Functions)

2.8A Graphing Absolute Value Functions

1. General form: y = a│x – h │ + k, a ≠ 0
2. The graph is shaped like a v.
3. Find the vertex: (h, k) (h is the opposite, not k)
4. Draw the line of symmetry: x = h (dotted line)
5. Use a as the slope to find a point on both sides of
the line of symmetry. ( Or do a t-chart with the
vertex being the middle point. Choose an x less
than h and an x greater than h.)
6. Draw the graph.

Example: y = 3│ x + 2│ – 5
 The vertex is ( -2, -5),
 The line of symmetry is x = -2
 The graph opens up because a > 0.
 The slope is 3, so start at the vertex and go up 3
and to the right 1.
 Go back to the vertex. This time go up 3 and to
the left 1.

Writing the equation for an
Absolute Value Function
1. Find the vertex (h,k)
2. Substitute this into the general form:
y = a│x – h │ + k
3. Find another point on the graph (x,y) and
substitute these values into the general form.
4. Solve for a.
5. Write your equation. This time only substitute
the values of a, h, and k.

Write the equation for this graph.
1. Vertex: (-2,0)
2. Find another point (0,2)
3. Substitute these into the
equation to find a.
2 = a│0 – (-2)│+ 0
2 = a │2│
2 = 2a
a=1
4. So the equation is:
y = 1│x + 2│
y =│x + 2│

2.8 b absolute value functions

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2.8 b absolute value functions