What is the directrix (x^2-4x-4)/2 ?

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

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directrix (x^2-4x-4)/2

directrix

\frac{x ^{2} - 4 x - 4}{2}

y = - \frac{9}{2}

Solution steps

Rewrite

y = \frac{x ^{2} - 4 x - 4}{2}

in the standard form

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

(h, k) = (2, - 4), p = \frac{1}{2}

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

(2, - 4)

y-coordinate

y = - 4 - p

y = - 4 - \frac{1}{2}

Refine

y = - \frac{9}{2}

y = \frac{x ^{4} - x ^{2} - 2 x - 1}{x ^{2} - x - 1}

y = 6 x^{2}

y = (x + 4)^{2} + 1

- \frac{1}{20} y^{2}

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