What is the directrix x^2-4x-5 ?

The directrix x^2-4x-5 is y=-37/4

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directrix x^2-4x-5

directrix

x^{2} - 4 x - 5

y = - \frac{37}{4}

Solution steps

Rewrite

y = x^{2} - 4 x - 5

in the standard form

4 \cdot \frac{1}{4} (y - (- 9)) = (x - 2)^{2}

(h, k) = (2, - 9), 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, - 9)

y-coordinate

y = - 9 - p

y = - 9 - \frac{1}{4}

Refine

y = - \frac{37}{4}

4 x^{2} + 12 x + 9

5 x^{2}

x^{2} + x - 1

y^{2} - 8 x + 2 y + 17 = 0

6 (x - 8)^{2} + 7