Answer
See the image below.
(a) Blue graph.
(b) Red graph.
(c) Green graph.
(d) Purple graph.
Work Step by Step
To graph the following functions we will use the parent function $y=x^2$ and apply transformations.
(a) $g(x)=x^2+1$, This means that we have to shift the parent function upwards by $1$ unit. And we will get the $Blue$ graph, shown in the image above.
(b) $g(x)=(x-1)^2$, This means that we have to shift the parent function to the right-hand side by $1$ unit. So, we will get the $Red$ graph, shown in the image above
(Note, the black dotted line in the image is parent function $y=x^2$)
(c) $g(x)=-x^2$. This time it simply means to reflect the parent function about $x$-axis, so we will get the $Green$ graph, shown in the image above.
(d) $g(x)=(x-1)^2+3$. In this case we have to apply $2$ transformations. (Note, it doesn't matter which one we apply first).
Let's apply the transformation in parentheses first, which means that we have to move the parent function to the right by $1$ unit.
Then apply the $+3$, which means to shift the previous function upwards by $3$ units.
At last we will have the $Purple$ graph, shown in the image above.
