What is the directrix 6x^2+7x-3 ?

The directrix 6x^2+7x-3 is y=-61/12

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directrix 6x^2+7x-3

directrix

6 x^{2} + 7 x - 3

y = - \frac{61}{12}

Solution steps

Rewrite

y = 6 x^{2} + 7 x - 3

in the standard form

4 \cdot \frac{1}{24} (y - (- \frac{121}{24})) = (x - (- \frac{7}{12}))^{2}

(h, k) = (- \frac{7}{12}, - \frac{121}{24}), 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{7}{12}, - \frac{121}{24})

y-coordinate

y = - \frac{121}{24} - p

y = - \frac{121}{24} - \frac{1}{24}

Refine

y = - \frac{61}{12}

x = - 4 y^{2}

y^{2} - 10 x + 4 y - 16 = 0

- 4 x^{2} + 6 x - 1

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

y = - 4 x^{2} - 4