What is the directrix 4x^2+16x-3 ?

The directrix 4x^2+16x-3 is y=-305/16

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directrix 4x^2+16x-3

directrix

4 x^{2} + 16 x - 3

y = - \frac{305}{16}

Solution steps

Rewrite

y = 4 x^{2} + 16 x - 3

in the standard form

4 \cdot \frac{1}{16} (y - (- 19)) = (x - (- 2))^{2}

(h, k) = (- 2, - 19), 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

(- 2, - 19)

y-coordinate

y = - 19 - p

y = - 19 - \frac{1}{16}

Refine

y = - \frac{305}{16}

x = 2 y^{2} - 1 - (5 y - 6)

x^{2} - 2 x - 4 y + 13 = 0

y = 18 x^{2} - 14 x + 9

y = + x^{2} - 3

x^{2} - 26 x + 65