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

The directrix 3x^2-x-2 is y=-13/6

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directrix 3x^2-x-2

directrix

3 x^{2} - x - 2

y = - \frac{13}{6}

Solution steps

Rewrite

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

in the standard form

4 \cdot \frac{1}{12} (y - (- \frac{25}{12})) = (x - \frac{1}{6})^{2}

(h, k) = (\frac{1}{6}, - \frac{25}{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{25}{12})

y-coordinate

y = - \frac{25}{12} - p

y = - \frac{25}{12} - \frac{1}{12}

Refine

y = - \frac{13}{6}

y = - 3 x^{2} - 12 x - 9

y = \frac{1}{8} x^{2}

- 2 x^{2} + 5 x - 6

4 x^{2} - 20 x - 24 y + 97 = 0

\frac{6 x}{7} \frac{4 x}{3}