What is the directrix (x^5+x^4+x^3+x^2+x+1)/(x^3+1) ?

The directrix (x^5+x^4+x^3+x^2+x+1)/(x^3+1) is y= 1/2

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directrix (x^5+x^4+x^3+x^2+x+1)/(x^3+1)

directrix

\frac{x ^{5} + x ^{4} + x ^{3} + x ^{2} + x + 1}{x ^{3} + 1}

y = \frac{1}{2}

Solution steps

Rewrite

y = \frac{x ^{5} + x ^{4} + x ^{3} + x ^{2} + x + 1}{x ^{3} + 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 = x^{2} - 15 x

- x^{2} + 8 x - 10

y = - 4 x^{2} - 12 x - 8

x^{2} + 16 y = 0

y = 4 x^{2} - 24 x - 30

What is the directrix (x^5+x^4+x^3+x^2+x+1)/(x^3+1) ?
The directrix (x^5+x^4+x^3+x^2+x+1)/(x^3+1) is y= 1/2