What is the directrix y=(x^4-x^2-2x-1)/(x^2-x-1) ?

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

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directrix y=(x^4-x^2-2x-1)/(x^2-x-1)

directrix

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

y = \frac{1}{2}

Solution steps

Rewrite

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

in the standard form

4 \cdot \frac{1}{4} (y - \frac{3}{4}) = (x - (- \frac{1}{2}))^{2}

(h, k) = (- \frac{1}{2}, \frac{3}{4}), 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

(- \frac{1}{2}, \frac{3}{4})

y-coordinate

y = \frac{3}{4} - p

y = \frac{3}{4} - \frac{1}{4}

Refine

y = \frac{1}{2}

y = 6 x^{2}

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

- \frac{1}{20} y^{2}

y = x^{2} - 4 x + 3

(x - 2)^{2} = 8 (y - 1)

What is the directrix y=(x^4-x^2-2x-1)/(x^2-x-1) ?
The directrix y=(x^4-x^2-2x-1)/(x^2-x-1) is y= 1/2