What is the directrix 3x-3x^2 ?

The directrix 3x-3x^2 is y= 5/6

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directrix 3x-3x^2

directrix

3 x - 3 x^{2}

y = \frac{5}{6}

Solution steps

Rewrite

y = 3 x - 3 x^{2}

in the standard form

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

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

(\frac{1}{2}, \frac{3}{4})

y-coordinate

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

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

Refine

y = \frac{5}{6}

y = 2 x^{2} - 12 x - 5

y^{2} = 36 x

- \frac{1}{2} x^{2} + 5 x - 2

(x - 4)^{2} = 4 (y + 2)

16 x^{2} - 25