What is the directrix 1/3 (x+2)^2-3 ?

The directrix 1/3 (x+2)^2-3 is y=-15/4

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directrix 1/3 (x+2)^2-3

directrix

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

y = - \frac{15}{4}

Solution steps

Rewrite

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

in the standard form:

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

(h, k) = (- 2, - 3), p = \frac{3}{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

(- 2, - 3)

y-coordinate

y = - 3 - p

y = - 3 - \frac{3}{4}

Refine

y = - \frac{15}{4}

x^{2} - 6 x + 5 y = - 34

y^{2} - 8 x = 0

x^{2} + 8 x + 18

(y - 2)^{2} = 12 (x + 1)

y = x^{2} - 5 x - 24