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

The directrix y=(x+2)^2-3 is y=-13/4

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

directrix

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

y = - \frac{13}{4}

Solution steps

Rewrite

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

in the standard form:

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

(h, k) = (- 2, - 3), 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

(- 2, - 3)

y-coordinate

y = - 3 - p

y = - 3 - \frac{1}{4}

Refine

y = - \frac{13}{4}

- 2 x^{2} + 12 x - 2

4 x^{2} - 8 x - 3

y = - 9 x^{2}

y - 2 = 3 (x - 5)^{2}

y = (x - 12)^{2}