Let's look at this one
y>x^2-6x+9
First you should recognise this as a parabola, concave up because of the invisable + in front of the x 2
x=-b/2a will give you the axis of symmetry, you can start there if you want to.
the vertex will be on the axis of symmetry so it you put in the x value that you just found into the equation you can find the y value of the vertex.
I wouldn't normally start there
I'd look for the roots of the equation, that is where it crosses the x axis, and the equation of the x axis is y=0
so you need to solve
0=x 2 -6x +9
this one you can factorise and solve that way, the other one you will need to use the quadratic formula to get the roots
-3*-3=9 and -3+-3=-6 so this can be factorised to
0=(x-3)(x-3)
x=3
There is only one root so x=3 must also have been the axis of symmetry.
If there had been 2 roots you could have sketched the graph now but we still only have 1 point and we need at least 2 more.
The obvious one to choose is x=0 and you find the y value (I would do this even if I did already have 3 points)
By symmetry you can also find the y value for x=6
Now you can sketch the parabola. Remember it is > so it will be a dashed line. The actual parabola will not be included in the answer because there is no = sign.
Now you have to test a point. If (0,0) isn't on the graph this is always an easy one to choose.
y>x^2-6x+9
0>0^2-6*0+9
0>9 true or false?
It is false so you have to shade the side of the parabola that does not include (0,0)
Try graphing this one and then move on to the second one.
You might find graphing really fun when you get the hang of it. I like graphing equations.
+118653 
