What is the directrix y=-1/12 x^2+x ?

The directrix y=-1/12 x^2+x is y=6

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directrix y=-1/12 x^2+x

directrix

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

y = 6

Solution steps

Rewrite

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

in the standard form

4 (- 3) (y - 3) = (x - 6)^{2}

(h, k) = (6, 3), p = - 3

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

(6, 3)

y-coordinate

y = 3 - p

y = 3 - (- 3)

Refine

y = 6

y^{2} = 2 x

y = 6 x^{2} - 15 x

y = x^{2} - x - 20

x^{2} = 2 y

x^{2} = 28 y