This past week in Pre Calculus 11 we finished unit 5: Graphing Inequalities and Systems of Equations and started unit 8: Absolute Value and Reciprocal Functions. Something I learned this week was piecewise notation and what it means. There is 3 sections to a parabola and it is divided whenever the line touches the x-axis. To find piecewise notation for a parabola we write out the original equation without the absolute value for whichever section(s) are above the x-axis and write the opposite for the sections below the x-axis. Here is an example of a parabola writing in piecewise notation (writing inside yellow box):

Piecewise notation essentially shows the different sections of the line on the graph and each sections domain. Here is an example of instead of a parabola it is a linear equation: