What is the directrix y=-x^2 ?

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directrix y=-x^2

directrix

y = - x^{2}

y = \frac{1}{4}

Solution steps

Rewrite

y = - x^{2}

in the standard form:

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

(h, k) = (0, 0), p = - \frac{1}{4}

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}{4})

Refine

y = \frac{1}{4}

y = 4 x^{2}

y = x^{2} + 8 x + 18

y^{2} = x + 1

y = \frac{x ^{4} - 1}{x ^{2} - 1}

(x - 2) (x + 1)