What is the directrix 2x^2-4 ?

The directrix 2x^2-4 is y=-33/8

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directrix 2x^2-4

directrix

2 x^{2} - 4

y = - \frac{33}{8}

Solution steps

Rewrite

y = 2 x^{2} - 4

in the standard form:

4 \cdot \frac{1}{8} (y - (- 4)) = (x - 0)^{2}

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

(0, - 4)

y-coordinate

y = - 4 - p

y = - 4 - \frac{1}{8}

Refine

y = - \frac{33}{8}

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

(y - 6)^{2} = 36 (x - 2)

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

y = x + x^{2}

4 x - 11 y^{2} = 0