What is the directrix y=x^2+9x+4 ?

The directrix y=x^2+9x+4 is y=-33/2

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directrix y=x^2+9x+4

directrix

y = x^{2} + 9 x + 4

y = - \frac{33}{2}

Solution steps

Rewrite

y = x^{2} + 9 x + 4

in the standard form

4 \cdot \frac{1}{4} (y - (- \frac{65}{4})) = (x - (- \frac{9}{2}))^{2}

(h, k) = (- \frac{9}{2}, - \frac{65}{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{65}{4})

y-coordinate

y = - \frac{65}{4} - p

y = - \frac{65}{4} - \frac{1}{4}

Refine

y = - \frac{33}{2}

(x + 1)^{2} = 2 (y + 2)

3 x^{2} + 4

3 x^{2} + 2

5 x^{2} + 7 y = 3

x = 4 y^{2} + 12 y + 9