What is the directrix x^2+x+1 ?

The directrix x^2+x+1 is y= 1/2

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directrix x^2+x+1

directrix

x^{2} + x + 1

y = \frac{1}{2}

Solution steps

Rewrite

y = 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}

4 + 2 x - x^{2}

\frac{1}{4} x^{2} + x - 8

x^{2} - 8 x - 240

- 2 x^{2} - 4 x + 34

2 x^{2} - 5 x + 5