What is the directrix y=-x^2-4x+6 ?

The directrix y=-x^2-4x+6 is y= 41/4

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directrix y=-x^2-4x+6

directrix

y = - x^{2} - 4 x + 6

y = \frac{41}{4}

Solution steps

Rewrite

y = - x^{2} - 4 x + 6

in the standard form

4 (- \frac{1}{4}) (y - 10) = (x - (- 2))^{2}

(h, k) = (- 2, 10), p = - \frac{1}{4}

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, 10)

y-coordinate

y = 10 - p

y = 10 - (- \frac{1}{4})

Refine

y = \frac{41}{4}

2 (x - 3)^{2} + 6

y = - 3 x^{2} + 12 x - 8

x^{2} - 6 x - 12 y - 51 = 0

(x + 3)^{2} = 8 (y - 2)

- 8 x^{2}