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 $y=(x-1)^{2} =f(x-1)$ by
shifting the graph of f to the right by 1 unit.
(graph: green, dotted )
3. To graph $y=\displaystyle \frac{1}{2}(x-1)^{2} =\frac{1}{2}f(x-1)$
by vertically shrinking the green graph by factor $\displaystyle \frac{1}{2}$
(yellow graph, dashed)
4. To graph $h(x)=\displaystyle \frac{1}{2}(x-1)^{2}-1 =\frac{1}{2}f(x-1)-1,$
lower the yellow graph by 1 unit.
some points:
$(1+0,\ \displaystyle \frac{1}{2}(0)-1)$, $(1\pm 1,\ \displaystyle \frac{1}{2}(1)-1),\ (1\pm 2,\ \displaystyle \frac{1}{2}(4)-1)$.
(graph: red )