What is the directrix 2x^2 ?

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directrix 2x^2

directrix

2 x^{2}

y = - \frac{1}{8}

Solution steps

Rewrite

y = 2 x^{2}

in the standard form:

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

(h, k) = (0, 0), 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, 0)

y-coordinate

y = 0 - p

y = 0 - \frac{1}{8}

Refine

y = - \frac{1}{8}

y = 12 x^{2} - 72 x + 77

4 - x - x^{2}

y = - 7 (x - 8)^{2} + 6

y = x^{2} - 9 x + 20

x^{2} - 6 x + 5 y = 34