What is the directrix y=x^2+6x+9 ?

The directrix y=x^2+6x+9 is y=-1/4

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directrix y=x^2+6x+9

directrix

y = x^{2} + 6 x + 9

y = - \frac{1}{4}

Solution steps

Rewrite

y = x^{2} + 6 x + 9

in the standard form

4 \cdot \frac{1}{4} (y - 0) = (x - (- 3))^{2}

(h, k) = (- 3, 0), 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, 0)

y-coordinate

y = 0 - p

y = 0 - \frac{1}{4}

Refine

y = - \frac{1}{4}

8 (x - 2) = (y + 3)^{2}

- x^{2} - 4 x - 4

y = x^{2} - 8 x

- x^{2} - 4 x + 2

y = x^{2} - 6 x