Write down the equation of the parabola and state its vertex if focus is (2,0) and directrix x=-2.

The definition of a parabola states that any point on the parabola is equidistant from the focus and the directrix.
The focus is $F=(2,0)$.
The directrix is $x=-2$.
The distance from $(x,y)$ to the focus is $d_F = \sqrt{(x-2)^2 + (y-0)^2}$.
The distance from $(x,y)$ to the directrix $x=-2$ is $d_D = |x - (-2)| = |x+2|$.
Equating these distances:

$$\sqrt{(x-2)^2 + y^2} = |x+2|$$

$$x^2 - 4x + 4 + y^2 = x^2 + 4x + 4$$

Subtract $x^2$ from both sides:

$$-4x + 4 + y^2 = 4x + 4$$

Subtract 4 from both sides:

$$-4x + y^2 = 4x$$

Add $4x$ to both sides:

$$y^2 = 4x + 4x$$ $$y^2 = 8x$$

This is the equation of the parabola.

The standard form for a horizontal parabola is $(y-k)^2 = 4p(x-h)$, where $(h,k)$ is the vertex.
Comparing $y^2 = 8x$ with $(y-k)^2 = 4p(x-h)$, we can write $y^2 = 8x$ as $(y-0)^2 = 8(x-0)$.
Therefore, $h=0$ and $k=0$.

The equation of the parabola is $\boxed{y^2 = 8x}$.
The vertex of the parabola is $\boxed{(0,0)}$.