What is the directrix y=(3x^3-6x^2)/(x-2) ?

The directrix y=(3x^3-6x^2)/(x-2) is y=-1/12

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directrix y=(3x^3-6x^2)/(x-2)

directrix

y = \frac{3 x ^{3} - 6 x ^{2}}{x - 2}

y = - \frac{1}{12}

Solution steps

Rewrite

y = \frac{3 x ^{3} - 6 x ^{2}}{x - 2}

in the standard form

4 \cdot \frac{1}{12} (y - 0) = (x - 0)^{2}

(h, k) = (0, 0), 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

(0, 0)

y-coordinate

y = 0 - p

y = 0 - \frac{1}{12}

Refine

y = - \frac{1}{12}

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

(x + 6)^{2} = - 20 (y - 5)

\frac{x ^{3}}{x}

x^{2} + 24 y = 0

- 0.0000848 x^{2} - 0.006005 x + 1.004

What is the directrix y=(3x^3-6x^2)/(x-2) ?
The directrix y=(3x^3-6x^2)/(x-2) is y=-1/12