



If we
put a minus sign in front of the absolute value stuff



on the
right side of the equation ... 


Y
=  X^{2}  4






The X
axis still acts like a mirror, 


but now
because of the minus sign, everything lives BELOW the X axis. 


Anything
that would be above the X axis, is reflected down. 








If we
have another number on the right side of the equation 


that is
NOT inside the absolute value lines ... 





Y
= X^{2}  4 + 2






Because
of the "+ 2" the mirror reflection does not happen at the
X axis. 


The
entire equation, including the reflection line moves UP 2. 








If we had
a  2 instead of a + 2, 


the whole
graph would move DOWN 2 units ... 











If we
have an inequality sign (< or
> or ³
or £)
instead of an equal sign, 


we: 





1) Graph
the equation like it had an equal sign. 





2) If the
inequality uses <
or >, make the line
dotted, 


otherwise
make the line solid. 





3) Pick
an (X, Y) point that is NOT on the equation line 


and see
if it makes the inequality true 





4) If the
point you chose in step 3 makes the inequality true 


shade the
side of the graph line that the point is on. 


If the
point you chose in step 3 makes the inequality NOT true 


shade the
side of the equation that the point is not on. 





Example: 


Y < X^{2}
 6


















copyright 2005 Bruce Kirkpatrick 
