What is the directrix y^2+4y+3 ?

The directrix y^2+4y+3 is x=-5/4

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directrix y^2+4y+3

directrix

y^{2} + 4 y + 3

x = - \frac{5}{4}

Solution steps

Rewrite

x = y^{2} + 4 y + 3

in the standard form

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

(h, k) = (- 1, - 2), p = \frac{1}{4}

Parabola is symmetric around the x-axis and so the directrix is a line parallel to the y-axis, a distance

- p

from the center

(- 1, - 2)

x-coordinate

x = - 1 - p

x = - 1 - \frac{1}{4}

Refine

x = - \frac{5}{4}

(x + 3)^{2} = 4 (y + 4)

y = - 6 (x - 8)^{2} - 4

3 x^{2} + 6 x - 45

- x^{2} - 4 x - 3

y^{2} = - 7 x