What is the directrix y=-4x^2-12x-8 ?

The directrix y=-4x^2-12x-8 is y= 17/16

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directrix y=-4x^2-12x-8

directrix

y = - 4 x^{2} - 12 x - 8

y = \frac{17}{16}

Solution steps

Rewrite

y = - 4 x^{2} - 12 x - 8

in the standard form

4 (- \frac{1}{16}) (y - 1) = (x - (- \frac{3}{2}))^{2}

(h, k) = (- \frac{3}{2}, 1), p = - \frac{1}{16}

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

(- \frac{3}{2}, 1)

y-coordinate

y = 1 - p

y = 1 - (- \frac{1}{16})

Refine

y = \frac{17}{16}

x^{2} + 16 y = 0

y = 4 x^{2} - 24 x - 30

8 y = x^{2}

x^{2} = 24 (y - 8)

x^{2} = 36 y