What is the directrix y=x^2+8x-5 ?

The directrix y=x^2+8x-5 is y=-85/4

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directrix y=x^2+8x-5

directrix

y = x^{2} + 8 x - 5

y = - \frac{85}{4}

Solution steps

Rewrite

y = x^{2} + 8 x - 5

in the standard form

4 \cdot \frac{1}{4} (y - (- 21)) = (x - (- 4))^{2}

(h, k) = (- 4, - 21), 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

(- 4, - 21)

y-coordinate

y = - 21 - p

y = - 21 - \frac{1}{4}

Refine

y = - \frac{85}{4}

(y - 0)^{2} = - 43 (x - 0)

y = x^{2} + 22

- 29 x^{2} + 1388 x - 10040

x = - 2 y^{2}

y^{2} - 6 y + 3