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

The directrix y=x^2-x-6 is y=-13/2

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directrix y=x^2-x-6

directrix

y = x^{2} - x - 6

y = - \frac{13}{2}

Solution steps

Rewrite

y = x^{2} - x - 6

in the standard form

4 \cdot \frac{1}{4} (y - (- \frac{25}{4})) = (x - \frac{1}{2})^{2}

(h, k) = (\frac{1}{2}, - \frac{25}{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{1}{2}, - \frac{25}{4})

y-coordinate

y = - \frac{25}{4} - p

y = - \frac{25}{4} - \frac{1}{4}

Refine

y = - \frac{13}{2}

+ x^{2} + 12

y = 5 x^{2} + 210 x - 34775

y^{2} - 6 y - 4 x + 5 = 0

(x + 2)^{2} = - 6 (y - 1)

y = - x^{2} + 5 x - 7