What is the directrix-2x^2-24x-54 ?

The directrix-2x^2-24x-54 is y= 145/8

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directrix-2x^2-24x-54

directrix

- 2 x^{2} - 24 x - 54

y = \frac{145}{8}

Solution steps

Rewrite

y = - 2 x^{2} - 24 x - 54

in the standard form

4 (- \frac{1}{8}) (y - 18) = (x - (- 6))^{2}

(h, k) = (- 6, 18), 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

(- 6, 18)

y-coordinate

y = 18 - p

y = 18 - (- \frac{1}{8})

Refine

y = \frac{145}{8}

x^{2} - 2 x - 3

y = (3 x - 7)^{2}

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

5 x^{2} - 15 x + 3

x^{2} + 10 x - 24