Graphing Absolute Value Equations

• The formula for graphing absolute value equations is y=a|x-h+k|. The point (h,k) is the vertex, point a determines how high or low on the y-axis the sytem will be, and point k also determines how far left or right on the x-axis the system will be.
• Point k: One thing to know about moving the system to the left or the right is that if point k is negative then you move to right. If point k is positive then you move to the left. The reason for this is because "standard form" is negative, which in turn makes +h negative.
• Point a: If point a is positive then the system moves up and if point a is negative, it moves down.
• If the equation has a slope of 1 and starts on point (0,0), it can be written simply as y=|x|.
• The higher the slope of the equation, the smaller the width of the system is.
• If the slope is a fraction, then the width of the system increases.