What is the directrix (4x^3+11x^2+4x+21)/(x+3) ?

The directrix (4x^3+11x^2+4x+21)/(x+3) is y= 55/8

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directrix (4x^3+11x^2+4x+21)/(x+3)

directrix

\frac{4 x ^{3} + 11 x ^{2} + 4 x + 21}{x + 3}

y = \frac{55}{8}

Solution steps

Rewrite

y = \frac{4 x ^{3} + 11 x ^{2} + 4 x + 21}{x + 3}

in the standard form

4 \cdot \frac{1}{16} (y - \frac{111}{16}) = (x - \frac{1}{8})^{2}

(h, k) = (\frac{1}{8}, \frac{111}{16}), p = \frac{1}{16}

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{1}{8}, \frac{111}{16})

y-coordinate

y = \frac{111}{16} - p

y = \frac{111}{16} - \frac{1}{16}

Refine

y = \frac{55}{8}

- \frac{1}{3} (x - 3) = (y + 5)^{2}

+ 2.5 t^{2} + 6 t

y = x^{2} + 6 x + 8

- 5 t^{2} + 20 t

y = - (x - 2)^{2} + 4

What is the directrix (4x^3+11x^2+4x+21)/(x+3) ?
The directrix (4x^3+11x^2+4x+21)/(x+3) is y= 55/8