What is the directrix y=3x^2+6x-12 ?

The directrix y=3x^2+6x-12 is y=-181/12

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directrix y=3x^2+6x-12

directrix

y = 3 x^{2} + 6 x - 12

y = - \frac{181}{12}

Solution steps

Rewrite

y = 3 x^{2} + 6 x - 12

in the standard form

4 \cdot \frac{1}{12} (y - (- 15)) = (x - (- 1))^{2}

(h, k) = (- 1, - 15), 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

(- 1, - 15)

y-coordinate

y = - 15 - p

y = - 15 - \frac{1}{12}

Refine

y = - \frac{181}{12}

(x - 5)^{2} = 20 (y - 5)

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

x = + \frac{17}{4} (y + 2)^{2}

(x - 3)^{2} = - 4 (y - 2)

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