What is the directrix x^2+16x+8 ?

The directrix x^2+16x+8 is y=-225/4

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directrix x^2+16x+8

directrix

x^{2} + 16 x + 8

y = - \frac{225}{4}

Solution steps

Rewrite

y = x^{2} + 16 x + 8

in the standard form

4 \cdot \frac{1}{4} (y - (- 56)) = (x - (- 8))^{2}

(h, k) = (- 8, - 56), 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

(- 8, - 56)

y-coordinate

y = - 56 - p

y = - 56 - \frac{1}{4}

Refine

y = - \frac{225}{4}

(x - 3)^{2} - 4

(y + 1.5)^{2} = 4 (x - 2)

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

14 x^{2}

y = \frac{- 4 x ^{2} + 24 x + 161}{25}