What is the directrix y=-3(x-2)(x+5) ?

The directrix y=-3(x-2)(x+5) is y= 221/6

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directrix y=-3(x-2)(x+5)

directrix

y = - 3 (x - 2) (x + 5)

y = \frac{221}{6}

Solution steps

Rewrite

y = - 3 (x - 2) (x + 5)

in the standard form

4 (- \frac{1}{12}) (y - \frac{147}{4}) = (x - (- \frac{3}{2}))^{2}

(h, k) = (- \frac{3}{2}, \frac{147}{4}), 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{3}{2}, \frac{147}{4})

y-coordinate

y = \frac{147}{4} - p

y = \frac{147}{4} - (- \frac{1}{12})

Refine

y = \frac{221}{6}

5 x^{2} + 4 x - 9

y^{2} + 4 y + 3

(x + 3)^{2} = 4 (y + 4)

y = - 6 (x - 8)^{2} - 4

3 x^{2} + 6 x - 45