To solve the exercise and complete the table, first replace the values of x given in the equation and in this way obtain their corresponding y values.
So, you have
[tex]\begin{gathered} x=2 \\ f(x)=(x-5)^2+1 \\ f(1)=(2-5)^2+1 \\ f(1)=(-3)^2+1 \\ f(1)=9+1 \\ f(1)=10 \\ \text{ Then, you have the coordinate pair} \\ (2,10) \end{gathered}[/tex]
[tex]\begin{gathered} x=3 \\ f(x)=(x-5)^2+1 \\ f(3)=(3-5)^2+1 \\ f(3)=(-2)^2+1 \\ f(3)=4+1 \\ f(3)=5 \\ \text{ Then, you have the coordinate pair} \\ (3,5) \end{gathered}[/tex]
[tex]\begin{gathered} x=4 \\ f(x)=(x-5)^2+1 \\ f(4)=(4-5)^2+1 \\ f(4)=(-1)^2+1 \\ f(4)=1+1 \\ f(4)=2 \\ \text{ Then, you have the coordinate pair} \\ (4,2) \end{gathered}[/tex]
[tex]\begin{gathered} x=5 \\ f(x)=(x-5)^2+1 \\ f(5)=(5-5)^2+1 \\ f(5)=(0)^2+1 \\ f(5)=0+1 \\ f(5)=1 \\ \text{ Then, you have the coordinate pair} \\ (5,1) \end{gathered}[/tex]
[tex]\begin{gathered} x=6 \\ f(x)=(x-5)^2+1 \\ f(6)=(6-5)^2+1 \\ f(6)=(1)^2+1 \\ f(6)=1+1 \\ f(6)=2 \\ \text{ Then, you have the coordinate pair} \\ (6,2) \end{gathered}[/tex]
So, the table function looks like this
Finally, plotting the points on the graph, you have
