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

The directrix 3x^2-4x-2 is y=-41/12

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directrix 3x^2-4x-2

directrix

3 x^{2} - 4 x - 2

y = - \frac{41}{12}

Solution steps

Rewrite

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

in the standard form

4 \cdot \frac{1}{12} (y - (- \frac{10}{3})) = (x - \frac{2}{3})^{2}

(h, k) = (\frac{2}{3}, - \frac{10}{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

(\frac{2}{3}, - \frac{10}{3})

y-coordinate

y = - \frac{10}{3} - p

y = - \frac{10}{3} - \frac{1}{12}

Refine

y = - \frac{41}{12}

x^{2} - 5 x - 6

y^{2} + 8 x - 6 y + 25 = 0

5 y = - (x - 3)^{2} - 25

x^{2} + 2 x

y = x^{2} - 8 x + 10