What is the directrix 4(x+2)^2+5 ?

The directrix 4(x+2)^2+5 is y= 79/16

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directrix 4(x+2)^2+5

directrix

4 (x + 2)^{2} + 5

y = \frac{79}{16}

Solution steps

Rewrite

y = 4 (x + 2)^{2} + 5

in the standard form:

4 \cdot \frac{1}{16} (y - 5) = (x - (- 2))^{2}

(h, k) = (- 2, 5), p = \frac{1}{16}

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, 5)

y-coordinate

y = 5 - p

y = 5 - \frac{1}{16}

Refine

y = \frac{79}{16}

9 y^{2} + 12 x = 0

2 y^{2} - 16 y + 72 = 20 x

\frac{1}{2} x^{2}

4 y^{2} - 3 x = 0

y^{2} + 8 x - 4 y + 20 = 0