Answer
The axis of symmetry is $x=$3.
domain: $(-\infty,\infty)$
range: $(-\infty,1]$
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.
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$f(x)=1-(x-3)^{2}$
$f(x)=-(x-3)^{2}+1$
1. opens down (a=$-1$).
2. vertex: (3, 1)$. $The axis of symmetry is $x=$3.
3. x-intercepts:
$0=-(x-3)^{2}+1$
$(x-3)^{2}=1$
$x-3=\pm 1$
$x=3\pm 1$
$x=2$ or $x=4$
4. y-intercept:
$f(0)=-(0-3)^{2}+1=-8$
The axis of symmetry is $x=$3.
domain: $(-\infty,\infty)$
range: $(-\infty,1]$
