Absolute Value is defined by The graph of
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 @ (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) (set what’s in the absolute value symbols to 0 and solve for x; gives you the x-coord. of the vertex, y-coord. is k. ) 2. Use the slope to plot another point to the RIGHT of the vertex. 3. Use symmetry to plot a 3 rd point 4. Complete the graph
Graph y = -|x + 2| + 3 1. V = (-2, 3) 2. Apply the slope a=-1 to that point 3. Use the line of symmetry x=-2 to plot the 3 rd point. 4. Complete the graph
Graph y = -|x - 1| + 1
Write the equation for:
• The vertex is @ (0, -3) • It has the form: • y = a |x - 0| - 3 So the equation is: y = 2|x| -3 • To find a: substitute the coordinate of a point (2, 1) in and solve • (or count the slope from the vertex to another point to the right) • Remember: a is positive if the graph goes up • a is negative if the graph goes down
Write the equation for: y = ½|x| + 3
Assignment
- Slides: 10