What is the directrix y=3x^2-x-4 ?

The directrix y=3x^2-x-4 is y=-25/6

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directrix y=3x^2-x-4

directrix

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

y = - \frac{25}{6}

Solution steps

Rewrite

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

in the standard form

4 \cdot \frac{1}{12} (y - (- \frac{49}{12})) = (x - \frac{1}{6})^{2}

(h, k) = (\frac{1}{6}, - \frac{49}{12}), 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

(\frac{1}{6}, - \frac{49}{12})

y-coordinate

y = - \frac{49}{12} - p

y = - \frac{49}{12} - \frac{1}{12}

Refine

y = - \frac{25}{6}

(x - h)^{2} = 4 p (y - k)

y^{2} + 8 x = 0

y = 2 x^{2} - 4 x + 15

x^{2} + 6 x + 8 y = 7

y = x^{2} - 6 x - 1