What is the directrix y=3x^2-18x+23 ?

The directrix y=3x^2-18x+23 is y=-49/12

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directrix y=3x^2-18x+23

directrix

y = 3 x^{2} - 18 x + 23

y = - \frac{49}{12}

Solution steps

Rewrite

y = 3 x^{2} - 18 x + 23

in the standard form

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

(h, k) = (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

(3, - 4)

y-coordinate

y = - 4 - p

y = - 4 - \frac{1}{12}

Refine

y = - \frac{49}{12}

y^{2} - 5 x + 12 y = - 16

3 y^{2} = 10 x

4 x^{2} - 5 x + 6

3 x^{2} + x - 5

(y - 0)^{2} = - 4 \cdot 0.01 (x - 0)