What is the directrix y=-1/2 (x+6)^2+8 ?

The directrix y=-1/2 (x+6)^2+8 is y= 17/2

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directrix y=-1/2 (x+6)^2+8

directrix

y = - \frac{1}{2} (x + 6)^{2} + 8

y = \frac{17}{2}

Solution steps

Rewrite

y = - \frac{1}{2} (x + 6)^{2} + 8

in the standard form:

4 (- \frac{1}{2}) (y - 8) = (x - (- 6))^{2}

(h, k) = (- 6, 8), p = - \frac{1}{2}

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

(- 6, 8)

y-coordinate

y = 8 - p

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

Refine

y = \frac{17}{2}

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

y = 5 x^{2} + 1

y = x^{2} + 9 x + 4

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

3 x^{2} + 4

What is the directrix y=-1/2 (x+6)^2+8 ?
The directrix y=-1/2 (x+6)^2+8 is y= 17/2