What is the directrix y=24x-3x^2 ?

The directrix y=24x-3x^2 is y= 577/12

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directrix y=24x-3x^2

directrix

y = 24 x - 3 x^{2}

y = \frac{577}{12}

Solution steps

Rewrite

y = 24 x - 3 x^{2}

in the standard form

4 (- \frac{1}{12}) (y - 48) = (x - 4)^{2}

(h, k) = (4, 48), 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

(4, 48)

y-coordinate

y = 48 - p

y = 48 - (- \frac{1}{12})

Refine

y = \frac{577}{12}

x = - 5 y^{2}

y = (- x - 1) (x + 3)

2 (y - 1)^{2} - 4

x = - \frac{1}{2} (y - 2)^{2} + 5

y = 48 x - 8 x^{2}