What is the standard form of f(x)=x(x+9)

f(x) = x(x+9)

Or y = x(x+9)
is a parabola of 2nd degree.

y =
x^2+9x

y = (x+9/2)^2-
(9/2)^2

y+81/4 =
(x+4.5)^2

y+20.25 =
(x+4.5)^2.

The standard form of this type of formula
is:

4a(y - k) = (x-h)^2 with its vertex  (x,y) at (h , k)
and focus a units above (h,k) Or  focus at (h , k+a).

So
the give parabola has its vertex at (-4.5 , -20.25) and focus at (-4.5 , -20.25+1/4) =
(-4.5 , -20.00)