What is the directrix y=(x+1)(x+2) ?

The directrix y=(x+1)(x+2) is y=-1/2

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directrix y=(x+1)(x+2)

directrix

y = (x + 1) (x + 2)

y = - \frac{1}{2}

Solution steps

Rewrite

y = (x + 1) (x + 2)

in the standard form

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

(h, k) = (- \frac{3}{2}, - \frac{1}{4}), 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

(- \frac{3}{2}, - \frac{1}{4})

y-coordinate

y = - \frac{1}{4} - p

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

Refine

y = - \frac{1}{2}

y = x^{2} + x + 1

y = x^{2} + x + 3

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

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

- 3 x^{2} + 6 x - 1