What is the directrix x^2+2y=0 ?

The directrix x^2+2y=0 is y= 1/2

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directrix x^2+2y=0

directrix

x^{2} + 2 y = 0

y = \frac{1}{2}

Solution steps

Rewrite

x^{2} + 2 y = 0

in the standard form:

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

(h, k) = (0, 0), p = - \frac{1}{2}

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

(0, 0)

y-coordinate

y = 0 - p

y = 0 - (- \frac{1}{2})

Refine

y = \frac{1}{2}

y = \frac{4 x ^{3} + 11 x ^{2} + 4 x + 21}{x + 3}

- 2 x^{2} - 12 x - 23

2 x = (y - 3)^{2} + 4

y = \frac{x ^{2}}{28} - \frac{5 x}{14} + \frac{333}{28}

y = 3 x^{2} + x - 1