Absolute Value is defined by:

The graph of this piecewise function consists of 2 rays, is V-shaped and opens up. To the left of x=0 the line is y = -x To the right of x = 0 the line is y = x Notice that the graph is symmetric in the y-axis because every point (x,y) on the graph, the point (-x,y) is also on it.

y = a |x - h| + k Vertex is at (h,k) & is symmetrical in the line x=h V-shaped If a < 0 the graph opens down (a is negative) If a > 0 the graph opens up (a is positive) The graph is wider if |a| < 1 (fraction < 1) The graph is narrower if |a| > 1 a is the slope to the right of the vertex (…-a is the slope to the left of the vertex)

To graph y = a |x - h| + k 1. Plot the vertex (h,k) 2. Set what’s in the absolute value symbols to 0 and solving for x, gives you the x-coordinate of the vertex. The y-coordinate is k. 3. Use the slope to plot another point to the RIGHT of the vertex. 4. Use symmetry to plot a 3 rd point 5. Complete the graph

Graph y = -|x + 2| V = (-2,3) 2. Apply the slope a=-1 to that point 3. Use the line of symmetry x=-2 to plot the 3rd point. 4. Complete the graph

Graph y = -|x - 1| + 1

Write the equation for:

So the equation is: y = 2|x| -3  The vertex is at (0, -3)  The equation needs to be in the form y = a | x – h | + k  Therefore, y = a | x – 0 | - 3  Find the slope to the right of the vertex to find ‘a’.  The equation is: y = 2 | x – 0 | - 3

Write the equation for: y = ½|x| + 3

Assignment - Absolute Value Worksheet 1