What is the directrix 48x-6x^2 ?

The directrix 48x-6x^2 is y= 2305/24

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directrix 48x-6x^2

directrix

48 x - 6 x^{2}

y = \frac{2305}{24}

Solution steps

Rewrite

y = 48 x - 6 x^{2}

in the standard form

4 (- \frac{1}{24}) (y - 96) = (x - 4)^{2}

(h, k) = (4, 96), 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

(4, 96)

y-coordinate

y = 96 - p

y = 96 - (- \frac{1}{24})

Refine

y = \frac{2305}{24}

2 x^{2} - x

x^{2} = - 10 y

x^{2} - 4

y = 2 x^{2} - 13 x - 7

x = 7 y^{2}