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

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

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directrix y=2x^2-2

directrix

y = 2 x^{2} - 2

y = - \frac{17}{8}

Solution steps

Rewrite

y = 2 x^{2} - 2

in the standard form:

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

(h, k) = (0, - 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

(0, - 2)

y-coordinate

y = - 2 - p

y = - 2 - \frac{1}{8}

Refine

y = - \frac{17}{8}

y = 4 x^{2} + 8 x - 20

2 x^{2} - 4 x + 15

y = - \frac{1}{8} x^{2}

y = 7 - 2 x - 3 x^{2}

x^{2} = - 20 y