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

The directrix x^2+2x-y=3 is y=-17/4

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directrix x^2+2x-y=3

directrix

y = - \frac{17}{4}

Solution steps

Rewrite

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

in the standard form

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

(h, k) = (- 1, - 4), 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

(- 1, - 4)

y-coordinate

y = - 4 - p

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

Refine

y = - \frac{17}{4}