Sorry I missed this when you asked. The algebraic expression for the two pieces is the piecewise function -- one part that has the exact equation that is given, and the the other part that is the opposite, ie. the negative of what is given. To determine where each part occurs, you need the x-intercepts as found in the video. You could test a point in each interval to see where the original function is positive or negative, and then 'flip' the parts that are negative with a negative sign in front.