2.8 a absolute value functions

2.8 a absolute value functions

• 1.
  2.8A Absolute ValueFunctions Today’s objective: 1. I will graph absolute value functions. 2. I will write an equation for an absolute value function.
• 2.
  2.8A Graphing AbsoluteValue 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 (dashed 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.
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  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.
• 4.
  Writing the equationfor 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.
• 5.
  Write the equationfor 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│