What is the directrix 3x^2+5x-4 ?

The directrix 3x^2+5x-4 is y=-37/6

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directrix 3x^2+5x-4

directrix

3 x^{2} + 5 x - 4

y = - \frac{37}{6}

Solution steps

Rewrite

y = 3 x^{2} + 5 x - 4

in the standard form

4 \cdot \frac{1}{12} (y - (- \frac{73}{12})) = (x - (- \frac{5}{6}))^{2}

(h, k) = (- \frac{5}{6}, - \frac{73}{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{5}{6}, - \frac{73}{12})

y-coordinate

y = - \frac{73}{12} - p

y = - \frac{73}{12} - \frac{1}{12}

Refine

y = - \frac{37}{6}

y = - x^{2} - 1

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

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

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

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