What is the directrix+12x^2-14x ?

The directrix+12x^2-14x is y=-197/48

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directrix+12x^2-14x

directrix

+ 12 x^{2} - 14 x

y = - \frac{197}{48}

Solution steps

Rewrite

y = 12 x^{2} - 14 x

in the standard form

4 \cdot \frac{1}{48} (y - (- \frac{49}{12})) = (x - \frac{7}{12})^{2}

(h, k) = (\frac{7}{12}, - \frac{49}{12}), 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{7}{12}, - \frac{49}{12})

y-coordinate

y = - \frac{49}{12} - p

y = - \frac{49}{12} - \frac{1}{48}

Refine

y = - \frac{197}{48}

y^{2} = 12 (x - 4)

2 x^{2} - 4 x - 9

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

x^{2} = 4 y + 8

\frac{9 x ^{2}}{2}