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

The directrix+6x^2+6x-12 is y=-325/24

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directrix+6x^2+6x-12

directrix

+ 6 x^{2} + 6 x - 12

y = - \frac{325}{24}

Solution steps

Rewrite

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

in the standard form

4 \cdot \frac{1}{24} (y - (- \frac{27}{2})) = (x - (- \frac{1}{2}))^{2}

(h, k) = (- \frac{1}{2}, - \frac{27}{2}), 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

(- \frac{1}{2}, - \frac{27}{2})

y-coordinate

y = - \frac{27}{2} - p

y = - \frac{27}{2} - \frac{1}{24}

Refine

y = - \frac{325}{24}

y^{2} = 20 (x - 10)

y = 3 x^{2} - 18 x + 23

y^{2} - 5 x + 12 y = - 16

3 y^{2} = 10 x

4 x^{2} - 5 x + 6