What is the directrix-x^2-6x-13 ?

The directrix-x^2-6x-13 is y=-15/4

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directrix-x^2-6x-13

directrix

- x^{2} - 6 x - 13

y = - \frac{15}{4}

Solution steps

Rewrite

y = - x^{2} - 6 x - 13

in the standard form

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

(h, k) = (- 3, - 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

(- 3, - 4)

y-coordinate

y = - 4 - p

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

Refine

y = - \frac{15}{4}

3 x^{2} - 6 x + 9

2.6 + 2.2 x - 0.6 x^{2}

3 x^{2} - 6 x + 3

x = (y - 2) (3 y + 3)

\frac{1}{4} (x + 2)^{2} - 9