What is the directrix y=x^2+6x+11 ?

The directrix y=x^2+6x+11 is y= 7/4

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directrix y=x^2+6x+11

directrix

y = x^{2} + 6 x + 11

y = \frac{7}{4}

Solution steps

Rewrite

y = x^{2} + 6 x + 11

in the standard form

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

(h, k) = (- 3, 2), 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, 2)

y-coordinate

y = 2 - p

y = 2 - \frac{1}{4}

Refine

y = \frac{7}{4}