Answer
please see image
(graph of g(x) is red)
.
Work Step by Step
1. Graph $f(x)=x^{2}$
...opens up, vertex at (0,0),
some points: $(0,0)$, $(\pm 1,1),\ (\pm 2,4)$.
(graph: blue, dashed)
Refer to Table 2.4 (page 279):
2. To graph $y=(x-2)^{2} =f(x-2)$ by
shifting the graph of f to the right by $2$ units.
(graph: green, dotted )
3. To graph $y=2(x-1)^{2} =2f(x-1)$
by vertically stretching the green graph by factor 2
(yellow graph, dashed)
4. To graph $h(x)=2(x-1)^{2}-1 =2f(x-1)-1,$
lower the yellow graph by 1 unit.
some points:
$(1+0,\ 2(0)-1)$, $(1\pm 1,\ 2(1)-1),\ (1\pm 2,\ 2(4)-1)$.
(graph: red )