There are many ways to graph.
Easiest way:
Use a graphing calculator.
2nd easiest way:
Use an online graphing calculator like desmos.com
A 3rd way is to make a table and pick some points. Like pick x = 0 and then compute to find the y value which is 27. Pick enough points so that you should be able to graph the parabola.
The 4th way is the way I think your teacher may want you to do it, by using completing the square.
x²-12x+27 can be rewritten:
x²-12x+27-36+36 =
x²-12x+36-9 =
(x-6)²-9
From this expression we can see that our graph is just a transformation of the parent graph x² that is shifted 6 to the right and 9 down.
So just take the graph x² (I hope you know what that graph looks like). Move it 6 units to the right. Then move it 6 units down and that is your graph!
