What is the directrix 1/4 (x+2)^2-9 ?

The directrix 1/4 (x+2)^2-9 is y=-10

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directrix 1/4 (x+2)^2-9

directrix

\frac{1}{4} (x + 2)^{2} - 9

y = - 10

Solution steps

Rewrite

y = \frac{1}{4} (x + 2)^{2} - 9

in the standard form:

4 \cdot 1 \cdot (y - (- 9)) = (x - (- 2))^{2}

(h, k) = (- 2, - 9), 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

(- 2, - 9)

y-coordinate

y = - 9 - p

y = - 9 - 1

Refine

y = - 10

y^{2} - 12 x + 36 = 0

x^{2} - 6 x + 16

x^{2} - 6 x + 18

(x - 3)^{2} = - 12 (y - 2)

3 x^{2} - 5