What is the directrix y=3x^2-x+5 ?

The directrix y=3x^2-x+5 is y= 29/6

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directrix y=3x^2-x+5

directrix

y = 3 x^{2} - x + 5

y = \frac{29}{6}

Solution steps

Rewrite

y = 3 x^{2} - x + 5

in the standard form

4 \cdot \frac{1}{12} (y - \frac{59}{12}) = (x - \frac{1}{6})^{2}

(h, k) = (\frac{1}{6}, \frac{59}{12}), 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

(\frac{1}{6}, \frac{59}{12})

y-coordinate

y = \frac{59}{12} - p

y = \frac{59}{12} - \frac{1}{12}

Refine

y = \frac{29}{6}

x = y^{2} - y - 42

x^{2} - 4 x - 8 y + 2 = 0

(3 x - 4) (4 x - 3) - 2 x

(x - 3)^{2} = - 12 y

x^{2} = 10 y