What is the directrix 3x^2-31x+56-(x-8) ?

The directrix 3x^2-31x+56-(x-8) is y=-257/12

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directrix 3x^2-31x+56-(x-8)

directrix

3 x^{2} - 31 x + 56 - (x - 8)

y = - \frac{257}{12}

Solution steps

Rewrite

y = 3 x^{2} - 31 x + 56 - (x - 8)

in the standard form

4 \cdot \frac{1}{12} (y - (- \frac{64}{3})) = (x - \frac{16}{3})^{2}

(h, k) = (\frac{16}{3}, - \frac{64}{3}), p = \frac{1}{12}

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{16}{3}, - \frac{64}{3})

y-coordinate

y = - \frac{64}{3} - p

y = - \frac{64}{3} - \frac{1}{12}

Refine

y = - \frac{257}{12}

y = - 2.1 x^{2} + 410 x - 1340

y = x^{2} - 10000 x - 24000000

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

y^{2} - 8 x - 4 y - 20 = 0

y = - \frac{1}{2} x^{2} - 2 x + 6

What is the directrix 3x^2-31x+56-(x-8) ?
The directrix 3x^2-31x+56-(x-8) is y=-257/12