What is the directrix 3y+4x=-2x^2-14 ?

The directrix 3y+4x=-2x^2-14 is y=-29/8

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directrix 3y+4x=-2x^2-14

directrix

y = - \frac{29}{8}

Solution steps

Rewrite

3 y + 4 x = - 2 x^{2} - 14

in the standard form

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

(h, k) = (- 1, - 4), p = - \frac{3}{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

(- 1, - 4)

y-coordinate

y = - 4 - p

y = - 4 - (- \frac{3}{8})

Refine

y = - \frac{29}{8}