What is the directrix y=x^2-x-20 ?

The directrix y=x^2-x-20 is y=-41/2

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directrix y=x^2-x-20

directrix

y = x^{2} - x - 20

y = - \frac{41}{2}

Solution steps

Rewrite

y = x^{2} - x - 20

in the standard form

4 \cdot \frac{1}{4} (y - (- \frac{81}{4})) = (x - \frac{1}{2})^{2}

(h, k) = (\frac{1}{2}, - \frac{81}{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{81}{4})

y-coordinate

y = - \frac{81}{4} - p

y = - \frac{81}{4} - \frac{1}{4}

Refine

y = - \frac{41}{2}

x^{2} = 2 y

x^{2} = 28 y

y = (3 x - 4) (4 x - 3) - 2 x

y = x^{2} + 4 x + 4

y = - x^{2} + 5