What is the directrix x^2-x-2 ?

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

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directrix x^2-x-2

directrix

x^{2} - x - 2

y = - \frac{5}{2}

Solution steps

Rewrite

y = x^{2} - x - 2

in the standard form

4 \cdot \frac{1}{4} (y - (- \frac{9}{4})) = (x - \frac{1}{2})^{2}

(h, k) = (\frac{1}{2}, - \frac{9}{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{9}{4})

y-coordinate

y = - \frac{9}{4} - p

y = - \frac{9}{4} - \frac{1}{4}

Refine

y = - \frac{5}{2}

2 x^{2} + 5 x - 7

10 y^{2} = 22 x

y \geq x^{2}

y = - x^{2}

y = 4 x^{2}