What is the directrix y=+(x+5)^2+3 ?

The directrix y=+(x+5)^2+3 is y= 11/4

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directrix y=+(x+5)^2+3

directrix

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

y = \frac{11}{4}

Solution steps

Rewrite

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

in the standard form:

4 \cdot \frac{1}{4} (y - 3) = (x - (- 5))^{2}

(h, k) = (- 5, 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

(- 5, 3)

y-coordinate

y = 3 - p

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

Refine

y = \frac{11}{4}

(y + 6)^{2} = \frac{15}{11} (x + 12)

(y + 6)^{2} = 9 (x - 1)

y^{2} + 10 x = 0

y = - \frac{1}{2} (x + 6)^{2} + 8

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