What is the directrix y=(x-1)(3x+1) ?

The directrix y=(x-1)(3x+1) is y=-17/12

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directrix y=(x-1)(3x+1)

directrix

y = (x - 1) (3 x + 1)

y = - \frac{17}{12}

Solution steps

Rewrite

y = (x - 1) (3 x + 1)

in the standard form

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

(h, k) = (\frac{1}{3}, - \frac{4}{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{1}{3}, - \frac{4}{3})

y-coordinate

y = - \frac{4}{3} - p

y = - \frac{4}{3} - \frac{1}{12}

Refine

y = - \frac{17}{12}

y = - x^{2} - 4 x + 6

2 (x - 3)^{2} + 6

y = - 3 x^{2} + 12 x - 8

x^{2} - 6 x - 12 y - 51 = 0

(x + 3)^{2} = 8 (y - 2)