What is the directrix y=x^2-5x-24 ?

The directrix y=x^2-5x-24 is y=-61/2

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directrix y=x^2-5x-24

directrix

y = x^{2} - 5 x - 24

y = - \frac{61}{2}

Solution steps

Rewrite

y = x^{2} - 5 x - 24

in the standard form

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

(h, k) = (\frac{5}{2}, - \frac{121}{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{5}{2}, - \frac{121}{4})

y-coordinate

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

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

Refine

y = - \frac{61}{2}

y = - 4 (x + 10)^{2} + 6

y^{2} - 12 y - 4 x + 28 = 0

\frac{6 x}{7} \cdot \frac{4 x}{3}

9 y^{2} - 6 y - 9 - x = 0

2 X^{2}