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

The directrix y=6x^2+12x is y=-145/24

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directrix y=6x^2+12x

directrix

y = 6 x^{2} + 12 x

y = - \frac{145}{24}

Solution steps

Rewrite

y = 6 x^{2} + 12 x

in the standard form

4 \cdot \frac{1}{24} (y - (- 6)) = (x - (- 1))^{2}

(h, k) = (- 1, - 6), 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

(- 1, - 6)

y-coordinate

y = - 6 - p

y = - 6 - \frac{1}{24}

Refine

y = - \frac{145}{24}

y = - 4 (x - 2)^{2} + 16

4 X^{2} + 12 X + 9

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

y^{2} - 4 y - 8 x - 12 = 0

- (y + 3)^{2} - 1