Start by finding the vertex, which is the point the parabola turns. The x value is -b/2a, which you have in your notes here. b = -8 and a = 2 and therefore the x value of the vertex is 2. Plug that in to find the y value, which is -2.
Start by plotting this point and the y intercept, which is 6. The parabola will be a U shape, which goes upwards starting at the vertex. If you draw that using the side with the y intercept, you can just mirror it on the other side of the vertex.