Answer
The axis of symmetry is $x=1$.
domain: $(-\infty,\infty)$
range: $[$2, $\infty)$
Work Step by Step
To graph $f(x)=a(x-h)^{2}+k$,
1. Determine whether the parabola opens upward or downward.
If $a>0$, it opens upward. If $a<0$, it opens downward.
2. Determine the vertex of the parabola. The vertex is $(h, k)$.
3. Find any x-intercepts by solving $f(x)=0$.
The function's real zeros are the x-intercepts.
4. Find the y-intercept by computing $f(0)$.
5. Plot the intercepts, the vertex, and additional points as necessary
Connect these points with a smooth curve that is shaped like a bowl or an inverted bowl.
------------------ $f(x)=(x-1)^{2}+2$
1. opens up (a=1)
2. vertex: $(1, 2).$The axis of symmetry is $x=1$.
3. x-intercepts:
$0=(x-1)^{2}+2$
$(x-1)^{2}=-2$
$x-1=\pm\sqrt{-2}$
$x=1\pm i\sqrt{2}$
No x-intercepts.
4. y-intercept:
$f(0)=(0-1)^{2}+2=3$
The axis of symmetry is $x=1$.
domain: $(-\infty,\infty)$
range: $[$2, $\infty)$