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

The directrix y=x^2-2x^2 is y= 1/4

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directrix y=x^2-2x^2

directrix

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

y = \frac{1}{4}

Solution steps

Rewrite

y = x^{2} - 2 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 = - \frac{1}{12} x^{2} + x

y^{2} = 2 x

y = 6 x^{2} - 15 x

y = x^{2} - x - 20

x^{2} = 2 y