What is the directrix y=-3x^2-12x-9 ?

The directrix y=-3x^2-12x-9 is y= 37/12

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directrix y=-3x^2-12x-9

directrix

y = - 3 x^{2} - 12 x - 9

y = \frac{37}{12}

Solution steps

Rewrite

y = - 3 x^{2} - 12 x - 9

in the standard form

4 (- \frac{1}{12}) (y - 3) = (x - (- 2))^{2}

(h, k) = (- 2, 3), 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, 3)

y-coordinate

y = 3 - p

y = 3 - (- \frac{1}{12})

Refine

y = \frac{37}{12}

y = \frac{1}{8} x^{2}

- 2 x^{2} + 5 x - 6

4 x^{2} - 20 x - 24 y + 97 = 0

\frac{6 x}{7} \frac{4 x}{3}

x^{2} - x - 6