What is the directrix y=7-2x-3x^2 ?

The directrix y=7-2x-3x^2 is y= 89/12

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directrix y=7-2x-3x^2

directrix

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

y = \frac{89}{12}

Solution steps

Rewrite

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

in the standard form

4 (- \frac{1}{12}) (y - \frac{22}{3}) = (x - (- \frac{1}{3}))^{2}

(h, k) = (- \frac{1}{3}, \frac{22}{3}), 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

(- \frac{1}{3}, \frac{22}{3})

y-coordinate

y = \frac{22}{3} - p

y = \frac{22}{3} - (- \frac{1}{12})

Refine

y = \frac{89}{12}

x^{2} = - 20 y

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

t^{2} + 2 t - 48

x^{2} + 9

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