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

The directrix y=-4x^2-4 is y=-63/16

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directrix y=-4x^2-4

directrix

y = - 4 x^{2} - 4

y = - \frac{63}{16}

Solution steps

Rewrite

y = - 4 x^{2} - 4

in the standard form:

4 (- \frac{1}{16}) (y - (- 4)) = (x - 0)^{2}

(h, k) = (0, - 4), 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

(0, - 4)

y-coordinate

y = - 4 - p

y = - 4 - (- \frac{1}{16})

Refine

y = - \frac{63}{16}

(x - 4)^{2} = - 8 (y + 3)

y^{2} + 33 = - 8 x - 23

x^{2} + 7 x + 12

- x^{2} + 1

- x^{2} + 7