What are the vertex, axis of symmetry, maximum or minimum value, domain, and range of...

Step 1
This is an equation of a parabola, so we can find all the requests easily.
${\displaystyle y={(x-5)}^2-9}$
${\displaystyle y-y_v=a{(x-x_v)}^2)}$
The vertex is ${\displaystyle V(5,-9)}$
The axis of symmetry is a vertical line passing from the vertex, so: ${\displaystyle x=5}$
The minimum is in the vertex (it is concave up!) and the maximum doesn't exist (it goes to ${\displaystyle +\mathrm{\infty }}$)
The domain is ${\displaystyle \mathbb{R}}$ because it is a polynomial function.
The range is ${\displaystyle [5,+\mathrm{\infty })}$
The x intercepts are points whose ordinate are 0, so:
${\displaystyle 0={(x-5)}^2-9\Rightarrow {(x-5)}^2=9\Rightarrow x-5=\pm 3\Rightarrow }$
${\displaystyle x=5\pm 3\Rightarrow A(8,0)}$ and ${\displaystyle B(2,0)}$
The y intercept is a point whose ascissa is 0, so:
${\displaystyle y={(0-5)}^2-9\Rightarrow 25-9=16\Rightarrow C(0,16)}$