What is the directrix y=-3x^2+12x-8 ?

The directrix y=-3x^2+12x-8 is y= 49/12

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directrix y=-3x^2+12x-8

directrix

y = - 3 x^{2} + 12 x - 8

y = \frac{49}{12}

Solution steps

Rewrite

y = - 3 x^{2} + 12 x - 8

in the standard form

4 (- \frac{1}{12}) (y - 4) = (x - 2)^{2}

(h, k) = (2, 4), p = - \frac{1}{12}

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

(2, 4)

y-coordinate

y = 4 - p

y = 4 - (- \frac{1}{12})

Refine

y = \frac{49}{12}

x^{2} - 6 x - 12 y - 51 = 0

(x + 3)^{2} = 8 (y - 2)

- 8 x^{2}

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

(y + 6)^{2} = \frac{15}{11} (x + 12)