(y+5)2=-6x+12 is graphed below:
Note that when y=-5 and x=2, both sides of the equation are zero. This indicates that (2,-5) is the vertex.
The y-intercept can be found by setting x=0 and solving for y:
(y+5)2=12, y+5=±√12=±2√3, that ia, approximately y=2√3-5=-1.54 and -8.46 approx.
The x-intercept is found by setting y=0 and solving for x:
52=-6x+12, 6x=12-25=-13, so the x-intercept=-13/6=-2.17 approx.
The curve has to pass through the intercepts and the vertex, so this helps you to sketch the graph.