What is the directrix y=x^2-6x-12 ?

The directrix y=x^2-6x-12 is y=-85/4

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directrix y=x^2-6x-12

directrix

y = x^{2} - 6 x - 12

y = - \frac{85}{4}

Solution steps

Rewrite

y = x^{2} - 6 x - 12

in the standard form

4 \cdot \frac{1}{4} (y - (- 21)) = (x - 3)^{2}

(h, k) = (3, - 21), 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

(3, - 21)

y-coordinate

y = - 21 - p

y = - 21 - \frac{1}{4}

Refine

y = - \frac{85}{4}

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

x^{2} - 8 x + \frac{63}{4}

x^{2} = - 2 y

\frac{1}{4} x^{2}

3 y^{2} - 30 y + 77