What is the directrix x^2-x-56 ?

The directrix x^2-x-56 is y=-113/2

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directrix x^2-x-56

directrix

x^{2} - x - 56

y = - \frac{113}{2}

Solution steps

Rewrite

y = x^{2} - x - 56

in the standard form

4 \cdot \frac{1}{4} (y - (- \frac{225}{4})) = (x - \frac{1}{2})^{2}

(h, k) = (\frac{1}{2}, - \frac{225}{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{225}{4})

y-coordinate

y = - \frac{225}{4} - p

y = - \frac{225}{4} - \frac{1}{4}

Refine

y = - \frac{113}{2}

y^{2} = 4 a x

y^{2} - 2 y - 4 x + 9 = 0

\frac{1}{3} x^{2} - \frac{8}{3} x + \frac{1}{3}

2 x^{2} - 7 x + 15

3 x^{2} - 12 x + 5