What is the directrix y=3x^2-12x+5 ?

The directrix y=3x^2-12x+5 is y=-85/12

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directrix y=3x^2-12x+5

directrix

y = 3 x^{2} - 12 x + 5

y = - \frac{85}{12}

Solution steps

Rewrite

y = 3 x^{2} - 12 x + 5

in the standard form

4 \cdot \frac{1}{12} (y - (- 7)) = (x - 2)^{2}

(h, k) = (2, - 7), 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

(2, - 7)

y-coordinate

y = - 7 - p

y = - 7 - \frac{1}{12}

Refine

y = - \frac{85}{12}

(y - 2)^{2} = k (x - 3)

y = - 5 (x - 4)^{2} + 180

x^{2} - 2 x + 2

- x^{2} - 3 x - 2

y = x^{2} + 7 x - 3