Answer
The axis of symmetry is $x=-2$.
domain: $(-\infty,\infty)$
range: $[-1,\infty)$
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.
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$f(x)=2(x+2)^{2}-1$
1. opens up (a=$+2$).
2. vertex: $(-2, -1). $The axis of symmetry is $x=-2$.
x-intercepts:
$0=2(x+2)^{2}-1$
2 $(x+2)^{2}=1$
$(x+2)^{2}=\displaystyle \frac{1}{2}$
$x+2=\displaystyle \pm\frac{1}{\sqrt{2}}$
$x=-2\displaystyle \pm\frac{1}{\sqrt{2}}=-2\pm\frac{\sqrt{2}}{2}$
y-intercept:
$f(0)=2(0+2)^{2}-1=7$
The axis of symmetry is $x=-2$.
domain: $(-\infty,\infty)$
range: $[-1,\infty)$
