What is the directrix+(2h^3+4h^2+5h)/h ?

The directrix+(2h^3+4h^2+5h)/h is y= 23/8

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directrix+(2h^3+4h^2+5h)/h

directrix

+ \frac{2 h ^{3} + 4 h ^{2} + 5 h}{h}

y = \frac{23}{8}

Solution steps

Rewrite

y = \frac{2 h ^{3} + 4 h ^{2} + 5 h}{h}

in the standard form

4 \cdot \frac{1}{8} (y - 3) = (h - (- 1))^{2}

(h, k) = (- 1, 3), p = \frac{1}{8}

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

(- 1, 3)

y-coordinate

y = 3 - p

y = 3 - \frac{1}{8}

Refine

y = \frac{23}{8}

What is the directrix+(2h^3+4h^2+5h)/h ?
The directrix+(2h^3+4h^2+5h)/h is y= 23/8