$f(x) = ax^2 + bx + c$

Plugging-in (0, 9);
$9 = a(0)^2 + b(0) + c$
$c = 9$

So, $f(x) = ax^2 + bx + 9$

Plugging-in (9, 0);
$0 = a(9)^2 + b(9) + 9$
$81a + 9b = -9$
$9a + b = -1$ ....... (1)

Plugging-in (7, 30);
$30 = a(7)^2 + b(7) + 9$
$49a + 7b = 21$
$7a + b = 3$ ....... (2)

Subtracting (1) and (2);

$9a + b = -1$
$7a + b = 3$

$2a = -4$
$a = -2$

Substituting $a = -2$ in (2);
$7(-2) + b = 3$
$b = 17$

Finally, $f(x) = -2x^2 + 17x + 9$
Axis of symmetry is given by $x = x_v$, where $x_v$ is the coordinate of the vertex

$x_v = \frac{-b}{2a} = \frac{-17}{2(-2)} = \frac{17}{4}$