What is the directrix+6x^2-54x+120 ?

The directrix+6x^2-54x+120 is y=-37/24

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directrix+6x^2-54x+120

directrix

+ 6 x^{2} - 54 x + 120

y = - \frac{37}{24}

Solution steps

Rewrite

y = 6 x^{2} - 54 x + 120

in the standard form

4 \cdot \frac{1}{24} (y - (- \frac{3}{2})) = (x - \frac{9}{2})^{2}

(h, k) = (\frac{9}{2}, - \frac{3}{2}), p = \frac{1}{24}

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{9}{2}, - \frac{3}{2})

y-coordinate

y = - \frac{3}{2} - p

y = - \frac{3}{2} - \frac{1}{24}

Refine

y = - \frac{37}{24}

y = 9 x^{2} + 6 x + 1

x^{2} + 4 x + 7

y = 2 x^{2} - 6 x + 4

\frac{( x - 5 ) ( x - 10 )}{50}

2 x^{2} - 12 x + 14 - 14 y = 0