What is the standard form of x2 10x y 200?

Let's say you want the standard form of the equation x2 + 10x + y + 20 = 0.

x2 + 10x + y + 20 = 0 (add 5 and subtract y to both sides)

x2 + 10x + 25 = -y + 5 (form the square to the left, and factor out -1 to the right)

(x + 5)2 = -(y - 5) which is in the standard form (x - h)2 = 4p(y - k), where (h, k) = (-5, 5) is the vertex, and 4p = -1 yields p = -1/4, so the parabola opens downward.