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

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

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directrix y=18x^2-6x+4

directrix

y = 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}

7 x^{2} - 7 x

y = + x^{2} + 8 x + 6

y = (x + 3) (x - 1)

(x + 3)^{2} = - 8 (y + 2)

y = 3 x^{2} + 4