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

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

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directrix y=x^2+x+1

directrix

y = 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}

y = x^{2} + x + 3

- 2 x = (y + 3)^{2} + 6

y = \frac{3 x ^{3} - 6 x ^{2}}{x - 2}

- 3 x^{2} + 6 x - 1

(x + 6)^{2} = - 20 (y - 5)