What is the directrix y=-12x^2+4x ?

The directrix y=-12x^2+4x is y= 17/48

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directrix y=-12x^2+4x

directrix

y = - 12 x^{2} + 4 x

y = \frac{17}{48}

Solution steps

Rewrite

y = - 12 x^{2} + 4 x

in the standard form

4 (- \frac{1}{48}) (y - \frac{1}{3}) = (x - \frac{1}{6})^{2}

(h, k) = (\frac{1}{6}, \frac{1}{3}), p = - \frac{1}{48}

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{1}{6}, \frac{1}{3})

y-coordinate

y = \frac{1}{3} - p

y = \frac{1}{3} - (- \frac{1}{48})

Refine

y = \frac{17}{48}

x = \frac{1}{12} y^{2}

x = - 4 (y - 7)^{2} + 7

2 y^{2} - 16 x = 0

(x + 2)^{2} - 4

y = \frac{1}{4} (x + 5)^{2} - 1