What is the directrix 4x^2+12x+9 ?

The directrix 4x^2+12x+9 is y=-1/16

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directrix 4x^2+12x+9

directrix

4 x^{2} + 12 x + 9

y = - \frac{1}{16}

Solution steps

Rewrite

y = 4 x^{2} + 12 x + 9

in the standard form

4 \cdot \frac{1}{16} (y - 0) = (x - (- \frac{3}{2}))^{2}

(h, k) = (- \frac{3}{2}, 0), 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}, 0)

y-coordinate

y = 0 - p

y = 0 - \frac{1}{16}

Refine

y = - \frac{1}{16}

5 x^{2}

x^{2} + x - 1

y^{2} - 8 x + 2 y + 17 = 0

6 (x - 8)^{2} + 7

y^{2} + 12 x + 8 y - 44 = 0