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

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

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

directrix

y = \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}

- 2 x^{2} - 12 x - 23

2 x = (y - 3)^{2} + 4

y = \frac{x ^{2}}{28} - \frac{5 x}{14} + \frac{333}{28}

y = 3 x^{2} + x - 1

y = x^{2} - 5 x + 6

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