What is the directrix (x-1)^2-2 ?

The directrix (x-1)^2-2 is y=-9/4

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directrix (x-1)^2-2

directrix

(x - 1)^{2} - 2

y = - \frac{9}{4}

Solution steps

Rewrite

y = (x - 1)^{2} - 2

in the standard form:

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

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

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

(1, - 2)

y-coordinate

y = - 2 - p

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

Refine

y = - \frac{9}{4}

y^{2} - 10 y + 4 x + 25 = 0

(x + 4)^{2} = - 6 (y - 3)

(x - 3)^{2} = \frac{1}{2} (y + 1)

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

(y + 1)^{2} = 2 (x - 5)