What is the directrix y=(-x-1)(x+3) ?

The directrix y=(-x-1)(x+3) is y= 5/4

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directrix y=(-x-1)(x+3)

directrix

y = (- x - 1) (x + 3)

y = \frac{5}{4}

Solution steps

Rewrite

y = (- x - 1) (x + 3)

in the standard form

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

(h, k) = (- 2, 1), 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, 1)

y-coordinate

y = 1 - p

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

Refine

y = \frac{5}{4}

2 (y - 1)^{2} - 4

x = - \frac{1}{2} (y - 2)^{2} + 5

y = 48 x - 8 x^{2}

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

y = - 2 x^{2}