This week we started the “Absolute value and reciprocal functions” unit. This first lesson focused mainly on the shape of the graph that will result from graphing an absolute value of both a line and a parabola.

When you graph the absolute value of an equation, any part of the line or parabola that may drop below the X axis (ie. is a negative value) will “flip up” to the positive section of the graph. When the previously negative section of the graph moves up into the positive section it should be COMPLETELY SYMMETRICAL to its previous position on the negative half of the graph and it resembles a “mirror image”. This is because the values are the same except positive, they are exactly the same distance from zero.

On a linear graph (has only a line, no parabola). There is one singular point where the graphs negative values are “flipped” so that they are positive, this point is referred to as the critical point, this causes the graph to look like a big “V” but this DOES NOT make it the same as a parabola, it is still a linear graph.