What is the directrix y=x^2+10x-96 ?

The directrix y=x^2+10x-96 is y=-485/4

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directrix y=x^2+10x-96

directrix

y = x^{2} + 10 x - 96

y = - \frac{485}{4}

Solution steps

Rewrite

y = x^{2} + 10 x - 96

in the standard form

4 \cdot \frac{1}{4} (y - (- 121)) = (x - (- 5))^{2}

(h, k) = (- 5, - 121), 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, - 121)

y-coordinate

y = - 121 - p

y = - 121 - \frac{1}{4}

Refine

y = - \frac{485}{4}

4 (x + 2)^{2} + 5

9 y^{2} + 12 x = 0

2 y^{2} - 16 y + 72 = 20 x

\frac{1}{2} x^{2}

4 y^{2} - 3 x = 0