What is the directrix y=x^2-10x-31 ?

The directrix y=x^2-10x-31 is y=-225/4

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directrix y=x^2-10x-31

directrix

y = x^{2} - 10 x - 31

y = - \frac{225}{4}

Solution steps

Rewrite

y = x^{2} - 10 x - 31

in the standard form

4 \cdot \frac{1}{4} (y - (- 56)) = (x - 5)^{2}

(h, k) = (5, - 56), 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

(5, - 56)

y-coordinate

y = - 56 - p

y = - 56 - \frac{1}{4}

Refine

y = - \frac{225}{4}

3 x^{2} - 24 x - 15

(x + 4)^{2} = 12 y - 24

x^{2} - 2 x - 9

y = x^{2} - 8

- 0.4 x^{2} - 5