To graph $y={(x-3)}^2+1$, shift the graph of $y=x^2$to the right________ units and then________ 1 unit.

We have given function is,

$y={(x-3)}^2+1$

1) To graph the function of$y=f\left(x\right)+d$using the graph of $y=f\left(x\right)$we will move the graph of $f\left(x\right)$ " d " units upward.

2) To graph the function of $y=f\left(x\right)-d$using the graph of $y=f\left(x\right)$ we will move the graph of $f\left(x\right)$ " d " units downward.

3) To graph the function of $y=f(x+c)$ using the graph of $y=f\left(x\right)$we will move the graph of $f\left(x\right)$ " c " units left.

4) To graph the function of $y=f(x-c)$ using the graph of $y=f\left(x\right)$we will move the graph of $f\left(x\right)$ " c " units Right.

We have given,

$y={(x-3)}^2+1$

To draw the graph of this function first we will graph the basic function $y=x^2$then we will draw the graph of $y={(x-3)}^2$moving the graph of $y=x^2$to 3 units right.

Finally to draw the graph of $y={(x-3)}^2+1$we will move the graph of $y={(x-3)}^2$to 1 unit upward.

Hence, to graph the $y={(x-3)}^2+1$, shift the graph of$y=x^2$to the right3unit andup to 1 unit.