What is the directrix y=-3x^2-42x-22 ?

The directrix y=-3x^2-42x-22 is y= 1501/12

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directrix y=-3x^2-42x-22

directrix

y = - 3 x^{2} - 42 x - 22

y = \frac{1501}{12}

Solution steps

Rewrite

y = - 3 x^{2} - 42 x - 22

in the standard form

4 (- \frac{1}{12}) (y - 125) = (x - (- 7))^{2}

(h, k) = (- 7, 125), p = - \frac{1}{12}

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

(- 7, 125)

y-coordinate

y = 125 - p

y = 125 - (- \frac{1}{12})

Refine

y = \frac{1501}{12}

+ (x - 2) = 3 (y - 5)^{2}

x^{2} - 2 x - 24

18 x^{2} - 64 x - 14 y + 150 = 0

2 x^{2} + 5 x

y = - \frac{1}{14} x^{2} + 2

What is the directrix y=-3x^2-42x-22 ?
The directrix y=-3x^2-42x-22 is y= 1501/12