Sketch graph of function f(x) = 2(x-1)^2 - 3

The question states: Determine the domain and range of the function f(x) = 2(x-1)^2 - 3 by sketching its graph.

I know how to determine D and R, though I forgot how to sketch parabolas on graph. I think I also forgot how to factor too...

So far I did the following:

f(x) = 2(x - 1)^2 - 3

0 = 2(x - 1)^2 - 3

0 = 2(x - 1)(x - 1) - 3

0 = 2x^2 - 1x -1x + 2 - 3

0 = 2x^2 - 2x - 1

What do I do from here? Is this correct so far, or did I mess up on the first line (with the 2)?