What is the directrix x^2+10x-24 ?

The directrix x^2+10x-24 is y=-197/4

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directrix x^2+10x-24

directrix

x^{2} + 10 x - 24

y = - \frac{197}{4}

Solution steps

Rewrite

y = x^{2} + 10 x - 24

in the standard form

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

(h, k) = (- 5, - 49), 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, - 49)

y-coordinate

y = - 49 - p

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

Refine

y = - \frac{197}{4}

x (4 - x)

5 x^{2} - 3 x + 3

y = (x - 3)^{2} + 4

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

y^{2} - 8 x + 2 y + 25 = 0