What is the directrix y=3x^2+6x-1 ?

The directrix y=3x^2+6x-1 is y=-49/12

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directrix y=3x^2+6x-1

directrix

y = 3 x^{2} + 6 x - 1

y = - \frac{49}{12}

Solution steps

Rewrite

y = 3 x^{2} + 6 x - 1

in the standard form

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

(h, k) = (- 1, - 4), 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

(- 1, - 4)

y-coordinate

y = - 4 - p

y = - 4 - \frac{1}{12}

Refine

y = - \frac{49}{12}

9 x^{2} + 24 x + 72 y + 16 = 0

y = x^{2} - 10 x + 5

y = x^{2} - 6 x + 9

x^{2} - 2 x + 8 y + 9 = 0

\frac{1}{20} x^{2}