Question

What is the standard form of the equation of this parabola `y^2+6y+x+10=0`?

Answer 1

$$y = \sqrt(-x-10+9) -3$$

Explanation:

$$(y+3)^2 = y^2+9+6y$$
$$y^2+6y = (y+3)^2-9$$
$$y^2+6y + x + 10 = (y+3)^2-9 + x + 10 = 0$$
$$(y+3)^2 = -x-10+9$$
$$y+3 = \sqrt(-x-10+9)$$
$$y = \sqrt(-x-10+9) -3$$