What is the directrix 8-3x-2x^2 ?

The directrix 8-3x-2x^2 is y= 37/4

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directrix 8-3x-2x^2

directrix

y = \frac{37}{4}

Solution steps

Rewrite

y = 8 - 3 x - 2 x^{2}

in the standard form

4 (- \frac{1}{8}) (y - \frac{73}{8}) = (x - (- \frac{3}{4}))^{2}

(h, k) = (- \frac{3}{4}, \frac{73}{8}), 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

(- \frac{3}{4}, \frac{73}{8})

y-coordinate

y = \frac{73}{8} - p

y = \frac{73}{8} - (- \frac{1}{8})

Refine

y = \frac{37}{4}