union means OR and you shade AWAY (obviously) from the points. You write as two inequalities (because they are not linked by any common answers.)
Writtien as U
1. rational inequalitities (a fraction)
2. quadratic inequalities (factor ect...)
3. linear inequalities (one that is not quadraic or rational ie; fraction)
4. absolute value inequalities
1. you set the stuff inside absolute value equal to the negative amount on the other side (in this case you flip the sign) and you set it equal normally.
2. you finish simplifying. you get a range for x.
3. you finish writing it in interval notation/ on a number line.
4. you don't find critical points/test intervals with absolute value.
discriminant: b sq. -4ac
-you have 2 imaginary solutions (complex conjugates)
-the graph is a U with no x-intercepts
-you have 1 real solution counted twice (double root)
-the graph is a U with 1 x-intercept
It can be 1. perfect square 2. positive non-perfect square
For both you get two real distict solutions. But the perfect sq. is rational while the non-perfect sq. is irrational. The first one is also factorable.
-When you graph it, you get 2 x-intercepts.