What is the directrix x^2+5x-24 ?

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

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directrix x^2+5x-24

directrix

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}

\frac{1}{24} y^{2}

y = 25 x^{2} - 70 x + 36

- 3 x^{2} + 5 x

y = - x^{2} - 4 x - 3

y = 2 x^{2} + 3 π