What is the directrix y=-3x^2-12x-17 ?

The directrix y=-3x^2-12x-17 is y=-59/12

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directrix y=-3x^2-12x-17

directrix

y = - 3 x^{2} - 12 x - 17

y = - \frac{59}{12}

Solution steps

Rewrite

y = - 3 x^{2} - 12 x - 17

in the standard form

4 (- \frac{1}{12}) (y - (- 5)) = (x - (- 2))^{2}

(h, k) = (- 2, - 5), 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, - 5)

y-coordinate

y = - 5 - p

y = - 5 - (- \frac{1}{12})

Refine

y = - \frac{59}{12}

3 x - 3 x^{2}

y = 2 x^{2} - 12 x - 5

y^{2} = 36 x

- \frac{1}{2} x^{2} + 5 x - 2

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