What is the directrix (x^3+6x^2+9x)/(x+3) ?

The directrix (x^3+6x^2+9x)/(x+3) is y=-5/2

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directrix (x^3+6x^2+9x)/(x+3)

directrix

\frac{x ^{3} + 6 x ^{2} + 9 x}{x + 3}

y = - \frac{5}{2}

Solution steps

Rewrite

y = \frac{x ^{3} + 6 x ^{2} + 9 x}{x + 3}

in the standard form

4 \cdot \frac{1}{4} (y - (- \frac{9}{4})) = (x - (- \frac{3}{2}))^{2}

(h, k) = (- \frac{3}{2}, - \frac{9}{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{3}{2}, - \frac{9}{4})

y-coordinate

y = - \frac{9}{4} - p

y = - \frac{9}{4} - \frac{1}{4}

Refine

y = - \frac{5}{2}

y^{2} + 4 x - 8 y + 12 = 0

7 x^{2} - 3

2 y^{2} - 8 x = 0

y = \frac{1}{4} x^{2}

y = 2 x^{2} - 2

What is the directrix (x^3+6x^2+9x)/(x+3) ?
The directrix (x^3+6x^2+9x)/(x+3) is y=-5/2