This unit we’ve been tackling inequalities. Here is a little explanation on how to graph them and how to communicate all the essential information through a graph.
First off, the dotted or solid line. No matter the shape, having a dotted or solid line is very important. It is paramount to remember that a dotted line is used when the variables CANNOT equal and the solid is when they CAN.
If we have x<1, we know x must be smaller than one and does not equal it. If we have 
Next off, is pretty simple. If there is only a degree of 1, then it is a straight line. If there is a degree of 2 or more the shape changes. If we have 
From here, it’s quite similar to graphing quadratic equations, except we’ll have to show what numbers will work as a variable. We do this by shading the part of the graph that contains the numbers which will make the variable correct.
Take the equation
Because this is in general form, we already have a y-intercept (+2) which will come in handy.
On top of this, since there is no (a) variable, we know the parabola will use the standard 1, 3, 5, 7… pattern.
Now we can factor to
This gives us x-intercepts of (-2) and (-1)
With these points on our graph, we can now fill in the blanks without doing any more work. If you really wanted to, you could convert to vertex form and get a vertex as well, but for something as simple as this, it’s a bit overkill.
Here is the finalized graph. It passes through all the points listed. But how do we know where to shade?
Simple! you have to test. The easiest testing point is (0,0) because they’re both zero. Nice and easy. We now plug this into our original formula to eliminate any chance for error.
This is 0<2 which is a true statement. You then shade wherever the true statement is found (either inside or outside the parabola.)
In this case, it’s outside the parabola so we shade outside!
Alright, that’s all from me. Thank you for reading.