What is the directrix y= 1/4 (x-1)^2-2 ?

The directrix y= 1/4 (x-1)^2-2 is y=-3

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

directrix

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

y = - 3

Solution steps

Rewrite

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

in the standard form:

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

(h, k) = (1, - 2), p = 1

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 - 1

Refine

y = - 3

25 x^{2} - 10 x - 200 y - 119 = 0

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

2 x^{2} (2 + 1)

y = x^{2} + 16 x + 64

(x - 6)^{2} = 8 (y + 4)