Answer
Refer to the blue graph below.
Work Step by Step
The given function can be written as:
$$y=(x^2-2x+1)+1$$
$$y=(x-1)^2+1$$
The parent function of this is $y=x^2$.
Note that in $y=x^2$, when $x$ is replaced by $x-1$, the function becomes $y=(x-1)^2$
This means that with $y=f(x)=x^2$ as the parent function, the given function is equivalent to $y=f(x-1)+1$
RECALL:
(i) The graph of $y=f(x-c)$ involves a horizontal shift of $c$ units to the right of the parent function $y=f(x)$.
(ii) The graph of $y=f(x)+k$ involves a vertical shift of $k$ units upward.
The given function has $c=1$ and $k=1$.
Thus, its graph involves a horizontal shift of one unit to the right and a vertical shift of one unit upward of the function $y=x^2$.
To graph the given function, perform the following steps:
(1) Graph the parent function $y=x^2$. Refer to the black graph below.
(2) Shift the graph of the parent function one unit to the right to obtain the graph of $y=(x-1)^2$. Refer to the green graph.
(3) Shift the graph of $y=(x-1)^2$ one unit upward to obtain the graph of $y=(x-1)^2+1$. Refer to the blue graph.
