What is the directrix y=(x-3)^2-2 ?

The directrix y=(x-3)^2-2 is y=-9/4

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directrix y=(x-3)^2-2

directrix

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

y = - \frac{9}{4}

Solution steps

Rewrite

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

in the standard form:

4 \cdot \frac{1}{4} (y - (- 2)) = (x - 3)^{2}

(h, k) = (3, - 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

(3, - 2)

y-coordinate

y = - 2 - p

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

Refine

y = - \frac{9}{4}

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

- x^{2} + 2 x - 3

y^{2} - 6 x + 6 y + 15 = 0

y = - 0.005 x^{2} + x + 5

y = x^{2} - 9 x + 3