What is the directrix 4x^2-12x-2 ?

The directrix 4x^2-12x-2 is y=-177/16

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directrix 4x^2-12x-2

directrix

4 x^{2} - 12 x - 2

y = - \frac{177}{16}

Solution steps

Rewrite

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

in the standard form

4 \cdot \frac{1}{16} (y - (- 11)) = (x - \frac{3}{2})^{2}

(h, k) = (\frac{3}{2}, - 11), p = \frac{1}{16}

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{3}{2}, - 11)

y-coordinate

y = - 11 - p

y = - 11 - \frac{1}{16}

Refine

y = - \frac{177}{16}

3 x^{2} + 4 x - 3

y = 600 - 10 x + 0.25 x^{2}

11 x^{2} + 13

- 2 (x + 3) = (y - 1)^{2}

2 y^{2} = - 5 x