What is the directrix x^2+8x+7 ?

The directrix x^2+8x+7 is y=-37/4

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directrix x^2+8x+7

directrix

x^{2} + 8 x + 7

y = - \frac{37}{4}

Solution steps

Rewrite

y = x^{2} + 8 x + 7

in the standard form

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

(h, k) = (- 4, - 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

(- 4, - 9)

y-coordinate

y = - 9 - p

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

Refine

y = - \frac{37}{4}

(y + 5)^{2} = 6 (x + 1)

2 x^{2} + 5

2 y^{2} - 44 x = 0

x = - \frac{3}{8} (y - 2)^{2} - 1

(y + 12)^{2} = 9 (x - 9)