What is the directrix (x+3)^2=-y ?

The directrix (x+3)^2=-y is y= 1/4

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directrix (x+3)^2=-y

directrix

(x + 3)^{2} = - y

y = \frac{1}{4}

Solution steps

Rewrite

(x + 3)^{2} = - y

in the standard form:

4 (- \frac{1}{4}) (y - 0) = (x - (- 3))^{2}

(h, k) = (- 3, 0), p = - \frac{1}{4}

Parabola is symmetric around the y-axis and so the directrix is a line parallel to the x-axis, a distance

- p

from the center

(- 3, 0)

y-coordinate

y = 0 - p

y = 0 - (- \frac{1}{4})

Refine

y = \frac{1}{4}

x^{2} + 4

x^{2} - 4 x + 5

y = \frac{1}{2} x^{2} + 9 x + 8

x = \frac{1}{4} y^{2}

y = - 3 (x + 2)^{2} + 5