What is the directrix y=x^2-6x-1 ?

The directrix y=x^2-6x-1 is y=-41/4

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directrix y=x^2-6x-1

directrix

y = x^{2} - 6 x - 1

y = - \frac{41}{4}

Solution steps

Rewrite

y = x^{2} - 6 x - 1

in the standard form

4 \cdot \frac{1}{4} (y - (- 10)) = (x - 3)^{2}

(h, k) = (3, - 10), 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

(3, - 10)

y-coordinate

y = - 10 - p

y = - 10 - \frac{1}{4}

Refine

y = - \frac{41}{4}

y^{2} + 6 y + 8 x + 25 = 0

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

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

y = 5 x^{2}

3 x^{2} - x + 5