Answer:
Vertex form:

Standard Form:

Explanation:
Well the vertex form of an equation is given in the form:
where (h, k) is the vertex, and by looking at the graph, you'll see the vertex is at (2, -3). So plugging this into the equation gives you:
. Now to find a which will determine the stretch/compression, you can substitute any point in (besides the vertex, because that'll result in (x-2) being 0). So I'll use the point (0, -1) which is the only point I think I can accurately determine by looking at the graph (besides (4, -1) since it's symmetric). Anyways I'll plug this in
Plug in (0, -1) as (x, y)

calculate inside the parenthesis

square the -2

Add 3 to both 3 to both sides

divide both sides by 4

This gives you the equation:

To convert this into standard form you simply expand the square binomial, you can use the foil method to achieve this, but it generally expands to:
.
Original equation:

expand square binomial:

Distribute the 1/2

Combine like terms:
