What is the directrix x^2+9x+20 ?

The directrix x^2+9x+20 is y=-1/2

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directrix x^2+9x+20

directrix

x^{2} + 9 x + 20

y = - \frac{1}{2}

Solution steps

Rewrite

y = x^{2} + 9 x + 20

in the standard form

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

(h, k) = (- \frac{9}{2}, - \frac{1}{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

(- \frac{9}{2}, - \frac{1}{4})

y-coordinate

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

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

Refine

y = - \frac{1}{2}

y = - 7 x^{2} - 3

x^{2} - 10

y^{2} + 36 x = 0

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

y = (x + 314)^{2}