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 = - \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}