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

The directrix y=(x+3)(x-1) is y=-17/4

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

directrix

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

y = - \frac{17}{4}

Solution steps

Rewrite

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

in the standard form

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

(h, k) = (- 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

(- 1, - 4)

y-coordinate

y = - 4 - p

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

Refine

y = - \frac{17}{4}

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

y = 3 x^{2} + 4

y = 2 x^{2} - 8 x + 4

3 - t^{2}

y = - 8 (x + 1)^{2}