Given:

The function is, y=x2−2x+2.

Graph:

Express the given function as follows.

y=x2−2x+2=x2−2x+1+1=(x−1)2+1

Thus, draw the graph of y=(x−1)2+1.

The standard graph of the function y=x2 is roughly drawn as shown below in Figure 1.

Then, draw the graph of y=(x−1)2, shift the graph y=x2 by 1 unit to the right. Thus, the graph of y=(x−1)2 is shown below in Figure 2.

From Figure 2, it is observed that Figure 1 is shifted 1 unit to the right.

To draw the graph of y=(x−1)2+1, shift the graph y=(x−1)2 by 1 unit upward. Thus, the graph of y=(x−1)2+1 is shown below in Figure 3.

Observe that Figure 3 is obtained from Figure 1 in such a way that it is shifted 1 unit to the right and then shifted 1 unit upward.