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

The directrix y=4(x-1)^2-2 is y=-33/16

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

directrix

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

y = - \frac{33}{16}

Solution steps

Rewrite

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

in the standard form:

4 \cdot \frac{1}{16} (y - (- 2)) = (x - 1)^{2}

(h, k) = (1, - 2), p = \frac{1}{16}

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}{16}

Refine

y = - \frac{33}{16}

- 2 - x + x^{2}

(x - 1)^{2} - 2

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

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

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