What is the directrix 3x^2-6x+9 ?

The directrix 3x^2-6x+9 is y= 71/12

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directrix 3x^2-6x+9

directrix

3 x^{2} - 6 x + 9

y = \frac{71}{12}

Solution steps

Rewrite

y = 3 x^{2} - 6 x + 9

in the standard form

4 \cdot \frac{1}{12} (y - 6) = (x - 1)^{2}

(h, k) = (1, 6), 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

(1, 6)

y-coordinate

y = 6 - p

y = 6 - \frac{1}{12}

Refine

y = \frac{71}{12}

2.6 + 2.2 x - 0.6 x^{2}

3 x^{2} - 6 x + 3

x = (y - 2) (3 y + 3)

\frac{1}{4} (x + 2)^{2} - 9

y^{2} - 12 x + 36 = 0