What is the directrix y=x^2-5x-6 ?

The directrix y=x^2-5x-6 is y=-25/2

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directrix y=x^2-5x-6

directrix

y = x^{2} - 5 x - 6

y = - \frac{25}{2}

Solution steps

Rewrite

y = x^{2} - 5 x - 6

in the standard form

4 \cdot \frac{1}{4} (y - (- \frac{49}{4})) = (x - \frac{5}{2})^{2}

(h, k) = (\frac{5}{2}, - \frac{49}{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{5}{2}, - \frac{49}{4})

y-coordinate

y = - \frac{49}{4} - p

y = - \frac{49}{4} - \frac{1}{4}

Refine

y = - \frac{25}{2}

y^{2} + 8 y + 4 x + 20 = 0

- x^{2} + 4

y = + 2 (x + 1)^{2} - 5

x - x^{2}

x^{2} + 2 x - 16 y + 65 = 0