What is the equation of a directrix of the parabola of x^2+ 4 x + 4 y - 4 = 2-0

You can rewrite the equation into the form
.. y = 1/(4p)*(x -h)^2 +k
In this form, (h, k) is the vertex and p is the distance from the focus to the vertex, or the vertex to the directrix.

.. x^2 +4x -6 = -4y . . . . . . . . . . . add -2-4y
.. (x +2)^2 -10 = -4y . . . . . . . . . . complete the square
.. (-1/4)*(x +2)^2 +2.5 = y . . . . . . the desired form

Then the distance from vertex (-2, 2.5) to the directrix is -1, which means the directrix is 1 unit above the vertex.

The equation of the directrix is y = 3.5.

So the first thing we do is to multiply the top equation by 3. the reason i want to do this is i notice there will be a 6y on both equations and can possibly add/subtract them. so we get 6y = -3x + 27. adding that and the second equation we get 6x = 27-15 which is 12. divide by 6 and we get 2. ∴ x = 2. substituting 2 into the first equation we get 2y = -2 + 9 which is 7. divide by 2 and we get 7/2. ∴ y = 7/2, x = 2.

2.9863 to the 60th power