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

The directrix y=-2x^2-2x-2 is y=-11/8

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directrix y=-2x^2-2x-2

directrix

y = - 2 x^{2} - 2 x - 2

y = - \frac{11}{8}

Solution steps

Rewrite

y = - 2 x^{2} - 2 x - 2

in the standard form

4 (- \frac{1}{8}) (y - (- \frac{3}{2})) = (x - (- \frac{1}{2}))^{2}

(h, k) = (- \frac{1}{2}, - \frac{3}{2}), p = - \frac{1}{8}

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

y-coordinate

y = - \frac{3}{2} - p

y = - \frac{3}{2} - (- \frac{1}{8})

Refine

y = - \frac{11}{8}

\frac{x ^{2}}{9} + \frac{y ^{2}}{16} = 1

x^{2} - y^{2} = 25

x^{2} + y^{2} = 100

y^{2} = - 14 x

16 x^{2} + y^{2} = 16