Answer
Refer to the blue graph belpw.
Work Step by Step
RECALL:
The graph of the function $f(x) = (x-h)^2+k$:
(1) has its center at $(h, k)$
(2) involves the following transformation of the parent function $y=x^2$:
(a) vertical shift of $|k|$ units, upward when $k\gt 0$, downward when $k \lt0$; and
(b) horizontal shift of $|h|$ units, to the right when $h\gt0$, to the left when $h\lt0$
The given equation has:
$h=2$ and $k=1$.
Thus, the graph of the given function has its vertex at $(2, 1)$ and involves a 2-unit shift to the right and a 1-unit shift upward of the parent function $y=x^2$.
Therefore, to graph the given function, perform the following steps:
(1) Graph the parent function $y=x^2$ using a table of values. (Refer to the red graph below.)
(2) Shift the red graph 2 units to the right and 1 unit upward. (Refer to the blue graph above.)
