What is the directrix x^2+2x-8 ?

The directrix x^2+2x-8 is y=-37/4

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directrix x^2+2x-8

directrix

x^{2} + 2 x - 8

y = - \frac{37}{4}

Solution steps

Rewrite

y = x^{2} + 2 x - 8

in the standard form

4 \cdot \frac{1}{4} (y - (- 9)) = (x - (- 1))^{2}

(h, k) = (- 1, - 9), 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

(- 1, - 9)

y-coordinate

y = - 9 - p

y = - 9 - \frac{1}{4}

Refine

y = - \frac{37}{4}

x^{2} + 2 x - 1

y^{2} - 16 x = 0

2 x^{2} - 8 x + 9

- 2 x^{2} + 64 x - 90

y = \frac{x ^{2} - 4 x - 1}{7}