What is the directrix y=x^2+16x+64 ?

The directrix y=x^2+16x+64 is y=-1/4

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directrix y=x^2+16x+64

directrix

y = x^{2} + 16 x + 64

y = - \frac{1}{4}

Solution steps

Rewrite

y = x^{2} + 16 x + 64

in the standard form

4 \cdot \frac{1}{4} (y - 0) = (x - (- 8))^{2}

(h, k) = (- 8, 0), 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, 0)

y-coordinate

y = 0 - p

y = 0 - \frac{1}{4}

Refine

y = - \frac{1}{4}

(x - 6)^{2} = 8 (y + 4)

y = - 3 x^{2} - 42 x - 22

+ (x - 2) = 3 (y - 5)^{2}

x^{2} - 2 x - 24

18 x^{2} - 64 x - 14 y + 150 = 0