What is the directrix 6x^2-6x ?

The directrix 6x^2-6x is y=-37/24

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directrix 6x^2-6x

directrix

6 x^{2} - 6 x

y = - \frac{37}{24}

Solution steps

Rewrite

y = 6 x^{2} - 6 x

in the standard form

4 \cdot \frac{1}{24} (y - (- \frac{3}{2})) = (x - \frac{1}{2})^{2}

(h, k) = (\frac{1}{2}, - \frac{3}{2}), p = \frac{1}{24}

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}{2}, - \frac{3}{2})

y-coordinate

y = - \frac{3}{2} - p

y = - \frac{3}{2} - \frac{1}{24}

Refine

y = - \frac{37}{24}

(x - \frac{5}{2})^{2} = 7 (y + 3.75)

y = - x^{2} + 8 x - 18

11 x^{2} - 8

y = 7 x^{2} + 5

x^{2} + 3 x + 4