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

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

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

directrix

\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 = 16 x^{2} + 1

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

y = \frac{6 x}{7} \frac{4 x}{3}

\frac{4 x ^{3} + 11 x ^{2} + 4 x + 21}{x + 3}

- \frac{1}{3} (x - 3) = (y + 5)^{2}

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