What is the directrix y=6x^2-15x ?

The directrix y=6x^2-15x is y=-113/12

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directrix y=6x^2-15x

directrix

y = 6 x^{2} - 15 x

y = - \frac{113}{12}

Solution steps

Rewrite

y = 6 x^{2} - 15 x

in the standard form

4 \cdot \frac{1}{24} (y - (- \frac{75}{8})) = (x - \frac{5}{4})^{2}

(h, k) = (\frac{5}{4}, - \frac{75}{8}), p = \frac{1}{24}

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{5}{4}, - \frac{75}{8})

y-coordinate

y = - \frac{75}{8} - p

y = - \frac{75}{8} - \frac{1}{24}

Refine

y = - \frac{113}{12}

y = x^{2} - x - 20

x^{2} = 2 y

x^{2} = 28 y

y = (3 x - 4) (4 x - 3) - 2 x

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