What is the directrix y=4x^2-24x-30 ?

The directrix y=4x^2-24x-30 is y=-1057/16

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directrix y=4x^2-24x-30

directrix

y = 4 x^{2} - 24 x - 30

y = - \frac{1057}{16}

Solution steps

Rewrite

y = 4 x^{2} - 24 x - 30

in the standard form

4 \cdot \frac{1}{16} (y - (- 66)) = (x - 3)^{2}

(h, k) = (3, - 66), 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

(3, - 66)

y-coordinate

y = - 66 - p

y = - 66 - \frac{1}{16}

Refine

y = - \frac{1057}{16}

8 y = x^{2}

x^{2} = 24 (y - 8)

x^{2} = 36 y

(x + 4)^{2} - 1

\frac{x ^{3} + 6 x ^{2} + 9 x}{x + 3}