Answer
Axis of symmetry:$ x=-4$
Domain: $(-\infty,\infty)$
Range: $(-2,\infty )$
Work Step by Step
Follow the procedure on page 332,
Graphing Quadratic Functions with Equations in Standard Form:
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.
$a=1$, so it opens upward.
2. Determine the vertex of the parabola.
The vertex is $(h, k)=(-4,-2)$. Axis of symmetry:$ x=-4$
3. Find any x-intercepts by solving $f(x)=0$.
$(x+4)^{2}-2=0$
$(x+4)^{2}=2$
$x+4=\pm\sqrt{2}$
$x=-4\pm\sqrt{2}$
4. Find the y-intercept by computing $f(0)$.
$f(0)=(0+4)^{2}-2=14$
5. Plot the intercepts, the vertex, and additional points as necessary. Connect these points with a smooth curve.
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Axis of symmetry:$ x=-4$
Domain: $(-\infty,\infty)$
Range: $(-2,\infty )$
