What is the directrix y=(x+6)(x-2) ?

The directrix y=(x+6)(x-2) is y=-65/4

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directrix y=(x+6)(x-2)

directrix

y = (x + 6) (x - 2)

y = - \frac{65}{4}

Solution steps

Rewrite

y = (x + 6) (x - 2)

in the standard form

4 \cdot \frac{1}{4} (y - (- 16)) = (x - (- 2))^{2}

(h, k) = (- 2, - 16), 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, - 16)

y-coordinate

y = - 16 - p

y = - 16 - \frac{1}{4}

Refine

y = - \frac{65}{4}

6 x^{2} + 7 x - 3

x = - 4 y^{2}

y^{2} - 10 x + 4 y - 16 = 0

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

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