What is the directrix y=2x(x-9)-(x-9) ?

The directrix y=2x(x-9)-(x-9) is y=-145/4

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directrix y=2x(x-9)-(x-9)

directrix

y = 2 x (x - 9) - (x - 9)

y = - \frac{145}{4}

Solution steps

Rewrite

y = 2 x (x - 9) - (x - 9)

in the standard form

4 \cdot \frac{1}{8} (y - (- \frac{289}{8})) = (x - \frac{19}{4})^{2}

(h, k) = (\frac{19}{4}, - \frac{289}{8}), p = \frac{1}{8}

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{19}{4}, - \frac{289}{8})

y-coordinate

y = - \frac{289}{8} - p

y = - \frac{289}{8} - \frac{1}{8}

Refine

y = - \frac{145}{4}

y = 2 x^{2} - 10 x + 12

- x^{2} + 14 x - 45

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

y^{2} = 6 x

- 4 x^{2} + 2 x + 2

What is the directrix y=2x(x-9)-(x-9) ?
The directrix y=2x(x-9)-(x-9) is y=-145/4