What is the directrix 18x^2-6x+4 ?

The directrix 18x^2-6x+4 is y= 251/72

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directrix 18x^2-6x+4

directrix

18 x^{2} - 6 x + 4

y = \frac{251}{72}

Solution steps

Rewrite

y = 18 x^{2} - 6 x + 4

in the standard form

4 \cdot \frac{1}{72} (y - \frac{7}{2}) = (x - \frac{1}{6})^{2}

(h, k) = (\frac{1}{6}, \frac{7}{2}), p = \frac{1}{72}

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}{6}, \frac{7}{2})

y-coordinate

y = \frac{7}{2} - p

y = \frac{7}{2} - \frac{1}{72}

Refine

y = \frac{251}{72}

x^{2} - 4 x - y + 3 = 0

y = - 3 (x - 2) (x + 5)

5 x^{2} + 4 x - 9

y^{2} + 4 y + 3

(x + 3)^{2} = 4 (y + 4)