Show that the curve with equation y=x^2-6x+9 and the line with equation y=-x do not intersect.

First, you equate the 2 equations to get this single quadratic equation (x^2-5x+9=0). And then evaluate the expression b^2-4ac. If b^2 -4ac is < 0 then they do not intersect. In our case b^2 -4ac is -9, which is < 0; therefore they do not intersect.