2.8 absolute value functions
- 1. 2.8 Absolute Value Functions Today’s objective: 1. I will learn characteristics of absolute value functions. 2. I will graph absolute value functions. 3. I will write the equation for an absolute value function.
- 2. 2.8 Absolute Value Functions y = a│x – h │ + k, a≠0 The graph is shaped like a v.
- 3. Find the vertex Vertex: (h, k) h is always the opposite of the # in the absolute value bars k is always the same as in the equation
- 4. Line of symmetry x=h Shown with a dashed vertical line.
- 5. Graph opens up or down If a > 0: the graph opens up. the vertex (h, k) is the minimum. If a < 0: the graph opens down. the vertex (h, k) is the maximum.
- 6. Is the graph wider, narrower, or the same width as y = │x│. Graph is narrower if │a │> 1. Graph is wider if 0 < │a │< 1. Graph is the same width if │a │ = 1.
- 7. Example: y = 3│ x + 2│ – 5 The vertex is ( -2, -5), because the opposite of 2 is -2, and k is – 5. The line of symmetry is x = -2 The graph opens up because a > 0. The graph is narrower because│a│= 3 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.
- 8. 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.
- 9. 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│