What is the directrix y=18x^2-14x+9 ?

The directrix y=18x^2-14x+9 is y= 451/72

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directrix y=18x^2-14x+9

directrix

y = 18 x^{2} - 14 x + 9

y = \frac{451}{72}

Solution steps

Rewrite

y = 18 x^{2} - 14 x + 9

in the standard form

4 \cdot \frac{1}{72} (y - \frac{113}{18}) = (x - \frac{7}{18})^{2}

(h, k) = (\frac{7}{18}, \frac{113}{18}), 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{7}{18}, \frac{113}{18})

y-coordinate

y = \frac{113}{18} - p

y = \frac{113}{18} - \frac{1}{72}

Refine

y = \frac{451}{72}

y = + x^{2} - 3

x^{2} - 26 x + 65

y^{2} + 2 y + 1 = - 2 x + 4

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

y = x^{2} - 6 x + 5