What is the directrix (x+2)^2-4 ?

The directrix (x+2)^2-4 is y=-17/4

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directrix (x+2)^2-4

directrix

(x + 2)^{2} - 4

y = - \frac{17}{4}

Solution steps

Rewrite

y = (x + 2)^{2} - 4

in the standard form:

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

(h, k) = (- 2, - 4), 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

(- 2, - 4)

y-coordinate

y = - 4 - p

y = - 4 - \frac{1}{4}

Refine

y = - \frac{17}{4}

y = \frac{1}{4} (x + 5)^{2} - 1

y = + (x + 6)^{2}

y = - 0.5 x^{2} - 3

4 x^{2} + 48 y + 12 x = 159

(x - 3)^{2} = - 8 (y + 2)