What is the directrix y=4x^2+8x-20 ?

The directrix y=4x^2+8x-20 is y=-385/16

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directrix y=4x^2+8x-20

directrix

y = 4 x^{2} + 8 x - 20

y = - \frac{385}{16}

Solution steps

Rewrite

y = 4 x^{2} + 8 x - 20

in the standard form

4 \cdot \frac{1}{16} (y - (- 24)) = (x - (- 1))^{2}

(h, k) = (- 1, - 24), 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

(- 1, - 24)

y-coordinate

y = - 24 - p

y = - 24 - \frac{1}{16}

Refine

y = - \frac{385}{16}

2 x^{2} - 4 x + 15

y = - \frac{1}{8} x^{2}

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

x^{2} = - 20 y

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