What is the directrix y=-6(x-8)^2-4 ?

The directrix y=-6(x-8)^2-4 is y=-95/24

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directrix y=-6(x-8)^2-4

directrix

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

y = - \frac{95}{24}

Solution steps

Rewrite

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

in the standard form:

4 (- \frac{1}{24}) (y - (- 4)) = (x - 8)^{2}

(h, k) = (8, - 4), p = - \frac{1}{24}

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, - 4)

y-coordinate

y = - 4 - p

y = - 4 - (- \frac{1}{24})

Refine

y = - \frac{95}{24}

3 x^{2} + 6 x - 45

- x^{2} - 4 x - 3

y^{2} = - 7 x

x = y^{2} - 4

y = x^{2} + 5 x - 14