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

The foci y=x^2+5x-24 is (-5/2 ,-30)

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foci y=x^2+5x-24

foci

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

(- \frac{5}{2}, - 30)

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 focus lies a distance

p

from the center

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

along the y-axis

(- \frac{5}{2}, - \frac{121}{4} + p)

= (- \frac{5}{2}, - \frac{121}{4} + \frac{1}{4})

Refine

(- \frac{5}{2}, - 30)

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

y = 2 x^{2} - 1 + 5 x

y = 9 x^{2} + 48 x + 64

x^{2} - 12 x + 35

4.905 x^{2} + 8 x - 30