What is the directrix y=x^2+4x-1 ?

The directrix y=x^2+4x-1 is y=-21/4

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directrix y=x^2+4x-1

directrix

y = x^{2} + 4 x - 1

y = - \frac{21}{4}

Solution steps

Rewrite

y = x^{2} + 4 x - 1

in the standard form

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

(h, k) = (- 2, - 5), 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, - 5)

y-coordinate

y = - 5 - p

y = - 5 - \frac{1}{4}

Refine

y = - \frac{21}{4}

y^{2} - 10 y - 12 x + 37 = 0

\frac{x}{25} - y^{2} = 1

y = x^{2} - 10 x - 31

3 x^{2} - 24 x - 15

(x + 4)^{2} = 12 y - 24